Register now to access 7 million high quality study materials (What's Course Hero?) Course Hero is the premier provider of high quality online educational resources. With millions of study documents, online tutors, digital flashcards and free courseware, Course Hero is helping students learn more efficiently and effectively. Whether you're interested in exploring new subjects or mastering key topics for your next exam, Course Hero has the tools you need to achieve your goals.
10 Pages
Chapter 14
Course: BUSINESS 201, Spring 2011School: MIT
Rating:
Word Count: 1002
Document Preview
BINOMIAL UN-11C A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 B C D E F G H I J K TWO-DATE OPTION PRICING Up Down 10% -3% Initial stock price Interest rate Exercise price 50 6% 50 Stock price Bond price 55 ### 1.06 <-- =$G$12*(1+$B$7) 1.06 50 <-- =$G$12*(1+$B$7) 1 48.5 ###...
Unformatted Document Excerpt
Coursehero >> Massachusetts >> MIT >> BUSINESS 201Course Hero has millions of student submitted documents similar to the one
below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.
Course Hero has millions of student submitted documents similar to the one
below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.
BINOMIAL UN-11C
A
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
B
C
D
E
F
G
H
I
J
K
TWO-DATE OPTION PRICING
Up
Down
10%
-3%
Initial stock price
Interest rate
Exercise price
50
6%
50
Stock price
Bond price
55
###
1.06
<-- =$G$12*(1+$B$7)
1.06
50
<-- =$G$12*(1+$B$7)
1
48.5
###
5
###
0
###
Call option
???
A
0.7692 <-- =(D16-D18)/(B12*(B3-B4))
B
Call price
-35.1959 <-- =((1+B3)*D18-(1+B4)*D16)/((1+B7)*(B3-B4))
3.2656 <-- =C21*B6+C23
State prices
qu
qd
0.6531 <-- =(B7-B4)/((1+B7)*(B3-B4))
0.2903 <-- =(B3-B7)/((1+B7)*(B3-B4))
Check: confirm that state prices
actually price the stock and the bond
1.06
###
50
###
Pricing a put and call using the state prices
Solving for the portfolio parameters: A is the number of shares and B is the number of bonds.
55*A + 108*B = 5
48.5*A + 108*B = 0
or:
A*stock*(1+up)+B*(1+interest)=max(stock*(1+up)-X,0)
A*stock*(1+down)+B*(1+interest)=max(stock*(1+down)-X,0)
The solution is:
check on state prices
call price
3.2656023
A
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
B
C
D
E
F
G
H
I
TWO-DATE BINOMIAL OPTION PRICING WITH STATE PRICES
Up
Down
Initial stock price
Interest rate
Exercise price
10%
-3%
State prices
qu
qd
0.6531 <-- =(B7-B4)/((1+B7)*(B3-B4))
0.2903 <-- =(B3-B7)/((1+B7)*(B3-B4))
50
6%
50
Call payoff
In up state
In down state
Call price
5 <-- =MAX($B$6*(1+B3)-$B$8,0)
0 <-- =MAX($B$6*(1+B4)-$B$8,0)
3.2656 <-- =$E$4*B11+$E$5*B12
Put payoff
In up state
In down state
Put price
0 <-- =MAX($B$8-(1+B3)*$B$6,0)
1.5 <-- =MAX($B$8-(1+B4)*$B$6,0)
0.4354 <-- =$E$4*B16+$E$5*B17
Put-call parity
Stock + put
Call + PV(X)
50.4354 <-- =B6+B18
50.4354 <-- =B13+B8/(1+B7)
Note about PV(X) in put-call parity:
In the continuous-time framework (the standard
Black-Scholes framework), PV(X) = X*Exp(-i*T).
Because the framework here is discrete time,
PV(X) also has to be discrete-time: PV(X) =
X/(1+i) .
J
UN-11H
A
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
B
C
D
E
F
G
H
I
J
K
THREE-DATE BINOMIAL OPTION PRICING
Up
Down
10%
-3%
Initial stock price
Interest rate
Exercise price
state prices
qu
qd
50
6%
50
0.6531 <-- =(B7-B4)/((1+B7)*(B3-B4))
0.2903 <-- =(B3-B7)/((1+B7)*(B3-B4))
Stock price
Bond price
60.50
1.1236
55
50
1.06
53.35
48.5
Call option price
=qu*E20+qd*E22
10.50
7.830
3.35
2.188
0.00
=qu*C21+qd*C23
=qu*E22+qd*E24
1.1236
1.06
47.05
5.749
1
1.1236
UN-11I
FIVE DATE EUROPEAN BINOMIAL OPTION PRICING
up
down
10%
-3%
initial stock price
interest rate
exercise price
state prices
qu
qd
50
6%
50
0.6531 <-- =(B7-B4)/((1+B7)*(B3-B4))
0.2903 <-- =(B3-B7)/((1+B7)*(B3-B4))
73.2050
Stock price
66.5500
60.5000
55.0000
50.0000
64.5535
58.6850
53.3500
48.5000
56.9245
51.7495
47.0450
50.1970
45.6337
44.2646
1.2625
Bond price
1.1910
1.1236
1.0600
1.0000
1.2625
1.1910
1.1236
1.0600
1.2625
1.1910
1.1236
1.2625
1.1910
1.2625
23.2050
Call price
19.3802
16.0002
13.0190
10.4360
14.5535
11.5152
8.8502
6.6593
6.9245
4.5797
3.0284
0.1970
0.1287
0.0000
Page 261
A
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
B
C
D
E
F
G
H
I
J
FIVE DATE EUROPEAN BINOMIAL OPTION PRICING
up
down
10%
-3%
initial stock price
interest rate
exercise price
state prices
qu
qd
50
6%
50
0.6531
0.2903
73.2050
stock price
66.5500
60.5000
64.5535
55.0000
58.6850
50.0000
53.3500
56.9245
48.5000
51.7495
47.0450
50.1970
45.6337
44.2646
1.2625
bond price
1.1910
1.1236
1.2625
1.0600
1.1910
1.0000
1.1236
1.2625
1.0600
1.1910
1.1236
1.2625
1.1910
1.2625
23.2050
call price
19.3802
16.0002
14.5535
13.0190
11.5152
10.4360
8.8502
6.9245
6.6593
4.5797
3.0284
0.1970
0.1287
0.0000
qu^(# up steps)*qd^(# down steps)
Terminal
stock
price
Terminal
payoff
73.2050 23.2050
Number Number
of "up" of "down"
steps
steps
4
0
State
price
0.1820
Number
of paths
1
Value =
payoff *
price *
# paths
4.2224 <-- =G49*F49*C49
64.5535 14.5535
3
1
0.0809
4
4.7078 <-- =G51*F51*C51
56.9245
6.9245
2
2
0.0359
6
1.4933 <-- =G53*F53*C53
50.1970
0.1970
1
3
0.0160
4
0.0126 <-- =G55*F55*C55
44.2646
0.0000
0
4
0.0071
1
0.0000 <-- =G57*F57*C57
Option value
Page 5
10.4360 <-- =SUM(H49:H57)
UN-11N
THREE DATE BINOMIAL OPTION PRICING FOR AMERICAN CALL/PUT
up
down
10%
-3%
initial stock price
interest rate
exercise price
state prices
qu
qd
50
6%
50
Stock price
0.6531 <-- =(B7-B4)/((1+B7)*(B3-B4))
0.2903 <-- =(B3-B7)/((1+B7)*(B3-B4))
Bond price
60.5000
1.1236
55.00
50
1.06
53.3500
1
48.50
1.1236
1.06
47.0450
1.1236
Call put option
10.5000
7.83
5.749
3.3500
2.19
0.0000
American option
=MAX(MAX(X-S*(1+u),0),qu*put_payoffuu+qd*put_payoffud)
0.0000
0
0.4354
0.0000
=MAX(MAX(X-S*(1+d),0),qu*put_payoffud+qd*put_payoffdd)
1.5
2.9550
=MAX(MAX(X-S,0),qu*put_valueu+qd*put_valued)
European put option
0.0000
0
0.2490
0.0000
0.8578
2.9550
State labels
uu
u
0
ud or du
d
dd
PICTURES IN BOOK
Stock price
American put payoffs
60.50
0.00
55
50
??
53.35
48.5
??
0.00
??
47.05
2.96
Page 269
A
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
B
C
D
E
F
AMERICAN BINOMIAL OPTION PRICING IN EXCEL
S
X
T
r
Sigma
n
60 Current stock price
60 Option exercise price
0.5000 Time to option exercise (in years)
8% Annual interest rate
30% Riskiness of stock
20 Number of subdivisions of T
American put price
American call price
#MACRO? <-- =AmericanPut(S,X,T,interest,sigma,n)
#MACRO? <-- =AmericanCall(S,X,T,interest,sigma,n)
European put price
European call price
#MACRO? <-- =EurPut(S, X,T,interest,sigma,n)
#MACRO? <-- =EurCall(S, X,T,interest,sigma,n)
Put-call parity?
Delta t, t
R = ert
0.0250 <-- =B5/B8
1.0020 <-- =EXP(B6*B17)
American put + Stock
American call + Bond
#MACRO? <-- =B10+B3
#MACRO? <-- American call price+X/R^n
European put + Stock
European call + Bond
#MACRO? <-- =B13+B3
#MACRO? <-- European call price+X/R^n
Page 7
A
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
B
C
D
E
F
G
H
I
CONVERGENCE OF BINOMIAL TO BLACK-SCHOLES
S
X
T
r
Sigma
n
60 Current stock price
50 Option exercise price
0.5000 Time to option exercise (in years)
8% Annual interest rate
30% Riskiness of stock
20 Number of subdivisions of T
European binomial call price
European binomial put price
### <-- =EurCall(S, X,interest,sigma,T,n)
### <-- =EurPut(S, X,interest,sigma,T,n)
Black-Scholes call price
Black-Scholes put price
### <-- =BSCall(S, X,interest,sigma,T)
### <-- =BSPut(S, X,interest,sigma,T)
Data table: As n gets large,
binomial price -> Black-Scholes
n -->
Binomial call Black-Scholes
#MACRO?
<-- The data table header in cell C20 is hidden
10
#MACRO?
###
50
#MACRO?
###
75
#MACRO?
###
100
#MACRO?
###
125
#MACRO?
###
150
#MACRO?
###
175
#MACRO?
###
200
#MACRO?
###
225
#MACRO?
###
250
#MACRO?
###
275
#MACRO?
###
300
#MACRO?
###
325
#MACRO?
###
350
#MACRO?
###
375
#MACRO?
###
400
#MACRO?
###
425
#MACRO?
###
450
#MACRO?
###
475
#MACRO?
###
500
#MACRO?
###
J
Convergence of Binomial to Black-Scholes
12.00
10.00
8.00
Binomial call #MACRO?
Black-Scholes
6.00
4.00
2.00
0.00
0
50
100
150
200
250
300
n = number of subdivisions of T
350
400
450
500
A
1
2
3
4
5
6
7
8
9
B
C
D
E
F
G
H
I
J
K
L
T IME-DEPENDENT EXERCISE PRICES
Initial stock price
Up
Down
Interest rate
100
10%
-5%
6%
Exercise prices
Date 1
100
Date 2
105
Date 3
112
State prices
qu
0.6918 <-- =(B6-B5)/((1+B6)*(B4-B5))
10 qd
0.2516 <-- =(B4-B6)/((1+B6)*(B4-B5))
11
12 Check
13 1/(qu+qd )
1.06 <-- =1/(B9+B10)
14 qu *(1+up)+qd *(1+down)
1 <-- =B9*(1+B4)+B10*(1+B5)
15
16
Stock price
17
121.000
18
110.000
19
100.000
104.500
20
95.000
21
90.250
22
23
24
Date 0
Date 1
Date 2
25
26
Value at each node
27
16.000
28
11.583
29
8.368
2.041
30
1.412
31
0.000
32
=MAX(qu*F29+qd*F31,MAX(D20-E4,0))
33
34
Early exercise?
35
yes
36
no
37
no
38
no
39
no
40
41
42
Illustration--Date 3 payoffs
43
44
45
46
47
48
49
50
51
52
exercise
16.000
53
PV
15.340
54
55
Illustration--Date 2 & 3 market values
56
16.000
57
58
2.041
59
60
0.000
61
62
exercise
0.000
63
PV
2.041
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
133.100
114.950
99.275
85.738
Date 3
=MAX(qu *H26+qd*H28,MAX(F17-E5,0))
21.100 <-- =MAX(H16-E6,0)
2.950 <-- =MAX(H18-E6,0)
0.000
0.000
=IF(qu*H26+q d*H28>=
MAX(F17-E5,0),"no","yes")
21.1000
2.9500
0.0000
0.0000
21.100
2.950
0.000
0.000
M
Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more.
Course Hero has millions of course specific materials providing students with the best way to expand
their education.
Below is a small sample set of documents:
Below is a small sample set of documents:
MIT - BUSINESS - 201
STOCK PRICE DATE, DAILY, 26OCT98-25OCT99DateSP500AbbottFordKelloggMicrosoft ATT26-Oct-98 1072.32 44.895348.646 32.985292.3754427-Oct-98 1065.34 44.2795 49.1301 32.4983 92.4375 44.687528-Oct-98 1068.09 45.3264 49.8237 31.8897 92.68754329-Oct-
MIT - BUSINESS - 201
UN-13BA123456789101112131415161718192021222324252627282930313233BCDEFGHIJKBlack-Scholes Option-Pricing FormulaSXrTSigma25 Current stock price25 Exercise price6.00% Risk-free rate of interest0.5 Time to
MIT - BUSINESS - 201
A123456789101112131415161718192021222324252627282930313233343536373839404142BCDEFGHIJTHE OPTION TO EXPANDYearCF of single machine0-1000Discount rate for machine cash flowsRiskless discount rateNPV
MIT - BUSINESS - 201
ABCDEFGHIJBlack-Scholes option pricing formulaSXrTSigmad1d250 Current stock price50 Exercise price10.00% Risk-free rate of interest1 Time to maturity of option (in years)25% Stock volatility0.5250 <- (LN(S/X)+(r+0.5*sigma^2)*T)/(sig
MIT - BUSINESS - 201
UN-11IA12345678910111213141516171819202122232425262728293031323334353637383940414243444546474849505152535455565758596061626364656667686970717273747576777879808182838485
MIT - BUSINESS - 201
UN-15BA1234567891011121314151617181920212223242526272829303132333435363738394041424344454647484950515253545556BCDEFGHBASIC DURATION CALCULATIONYTMYear123456789107%Ct,A707070
MIT - BUSINESS - 201
UN-16CA1234567891011121314151617181920212223242526272829303132333435363738394041424344454647BCDEFGHIBASIC IMMUNIZATION EXAMPLE WITH 3 BONDSYield to maturity6%Coupon rateMaturityFace valueBond
MIT - BUSINESS - 201
McCULLOGH'S TERM STRUCTURE DATA SETDate1.19802.19803.19804.19805.19806.19807.19808.19809.198010.198011.198012.19801.19812.19813.19814.19815.19816.19817.19818.19819.198110.198111.198112.19811.19822.19823.19824.19825.19826.198
MIT - BUSINESS - 201
UN-new chapter 17, AA1234567891011BCDEFEXPECTED RETURN ON A ONE-YEAR BONDWITH AN ADJUSTMENT FOR DEFAULT PROBABILITYFace value, FPrice, PAnnual coupon rate, QNondefault probability, Recovery percentage, Expected cash flowExpected
MIT - BUSINESS - 201
UN-17BABCDEFGHIJKTcMrPayments per yeargDuration-continuous timeL27%256.0%41.256897 <- =(c_/r_*(1-EXP(-r_*(M-T_)+EXP(-r_*(M-T_)/(c_/0.08*(1-EXP(-0.08*(M-T_)+EXP(-0.08*(M-T_)13.32712 <- =(EXP(r_)*(-c_+c_*EXP(M*r_)-c_*M*r_+M*r_^2)/(
MIT - BUSINESS - 201
Page 432A1234567891011121314150.56430.92190.47250.72770.80050.01280.97480.41280.9670B0.85070.52730.88680.10370.18460.02580.05440.59690.1379CDE0.50780.01300.83450.35170.48280.32060.62440.19990.02120.8786 <- R
MIT - BUSINESS - 201
UN-19J1234567891011121314151617181920212223242526ACF1Growth rateDiscount rateYearCash flowNPVIRRBC23410%15%0-1150.00DE=C6*(1+$B$2)1234.002257.40FGH5342.606376.86IJ=D6*(1+$B$2)3283.144311.4574
MIT - BUSINESS - 201
UN-20EABC12345 Matrix A (a row vector)234678910 Matrix D (a 4 x 3 matrix)13-8-311-810-112-3-11113013314DEFGHIMATRICES IN EXCELMatrix B (a square 3 x 3 matrix)13-8-3-810-1-3-111Matrix C(a columnvector)13
MIT - BUSINESS - 201
UN-21AA123456789101112131415BCDEFGHGAUSS-SEIDEL METHOD-SOLUTION BY ITERATIVE SUBSTITUTIONy=(E4-2)/4x050.753.8750.46875 4.2968750.5742188 4.13867190.534668 4.1979980.5494995 4.17575070.5439377 4.18409350.5460234 4.18096
MIT - BUSINESS - 201
UN-22BA1234567891011121314BCDEFGEXCEL'S NPV FUNCTIONDiscount rateYearCash flowNPV10%0-100135233334425516334425516$11.65 <- =NPV(B3,C5:G5)+B5EXCEL'S IRR FUNCTIONYearCash flowIRR0-10013523315.00% <- =
MIT - BUSINESS - 201
ABCDEFG1 AUTO FILL/COPY212325 <- B3+3435465768798101112 Double-clicking on the "fill handle" of a cell will fill in the rest of the column13 provided there's a filled cell next to it.A123PUTTING LINE BREAKS IN CELLSThis
MIT - BUSINESS - 201
A123456BCDEFGHIJKFunctions in ActionParameterFunction11.25#MACRO? <- =Function1(B3)Placing the cursor on a cell with a small red triangle in the corner willshow you the source code of the function used in the cell.To edit the code
MIT - BUSINESS - 201
A1234567891011121314151617181920212223242526272829303132BCDEFGHIJKFunctions In ActionParameter Function1.1667 #MACRO? <- =Function1(A4)1.1667 #MACRO? <- =Function2(A5)1.16666 #MACRO? <- =Function1(A6)1.1666
MIT - BUSINESS - 201
AB123ActivecellDemo()4ActivecellDemo1()CDEFGHIJActivecell Macros in this Workbook5Placing the cursor on a cell with a small red triangle in the cornerwill show you the source code of the Macro or FunctionTo edit the code you may press
MIT - BUSINESS - 201
UN-15I2.6T erm Structures, 19482.42.2Pur e discount r a t e %21.81.61.41.210.80mo 1mo 2mo 3mo 4mo 5mo 6mo 9mo1yrMat urit y2 yr3yr4yr5yr10yr 15yr 20yrUN-15J18T erm Structures, 19811716Pur e discount r a t e, %1514131211109
Colorado Tech - ADMON - mpm
Universidad VirtualAdministracin de la Cadena de Valor2.4 Realizar reflexin tema SustentabilidadEQUIPO 37Olga Nora Garca Esquivel A00372979Tatiana Vanessa Mndez Martnez A01304717Amilcar Estrada Rodrguez A01304897Octavio Navarro Daz A01307499Alejan
Colorado Tech - ADMON - mpm
Reflexin sobre el artculo de la Biblioteca Digital Sustainable Operations Management",de Paul R Kleindorfer, Kalyan Singhal, Luk N Van Wassenhove. Production andOperations Management. Muncie: Winter 2005. Vol. 14, Iss. 4; pg. 482, 11 pgsEn la actualida
Colorado Tech - ADMON - mpm
cha06369_tn07.qxd2/12/037:01 PMPage 299TECHNICAL NOTE SEVENtechnical notetechnical note sevenP R O C E S S C A PA B I L I T Y A N DS TAT I S T I C A L Q U A L I T YCONTROLAssignable variation definedCommon variation definedVariation around Us
Colorado Tech - ADMON - mpm
Universidad VirtualAdministracin de la Cadena de Valor2.4 Realizar reflexin tema SustentabilidadEQUIPO 37Olga Nora Garca Esquivel A00372979Tatiana Vanessa Mndez Martnez A01304717Amilcar Estrada Rodrguez A01304897Octavio Navarro Daz A01307499Alejan
Colorado Tech - ADMON - mpm
LOOKING FOR.SOLUTIONSMANUAL ORTEST BANK ?OVER 10,000 TITLESAVALABLE!Student.Plus@Hotmail.Comwww.student-plus.netThe List Below Updated On 24, JULY, 2010How To Order? Email UsEmail us at STUDENT.PLUS@HOTMAIL.COM asking for the teaching or studyi
Colorado Tech - ADMON - mpm
Universidad VirtualAdministracin de la Cadena de Valor2.5 Resolver problemas del captulo 6EQUIPO 37Olga Nora Garca Esquivel A00372979Tatiana Vanessa Mndez Martnez A01304717Amilcar Estrada Rodrguez A01304897Octavio Navarro Daz A01307499Alejandro Be
Colorado Tech - ADMON - mpm
Universidad VirtualAdministracin de la Cadena de Valor2.4 Realizar reflexin tema SustentabilidadEQUIPO 37Olga Nora Garca Esquivel A00372979Tatiana Vanessa Mndez Martnez A01304717Amilcar Estrada Rodrguez A01304897Octavio Navarro Daz A01307499Alejan
Colorado Tech - ADMON - mpm
Universidad VirtualAdministracin de la Cadena de Valor2.4 Realizar reflexin tema SustentabilidadEQUIPO 37Olga Nora Garca Esquivel A00372979Tatiana Vanessa Mndez Martnez A01304717Amilcar Estrada Rodrguez A01304897Octavio Navarro Daz A01307499Alejan
Colorado Tech - ADMON - mpm
Colorado Tech - ADMON - mpm
TATIANA V. MENDEZA01304717ADMINISTRACION DE LA CADENA DE VALORPROBLEMA 2Rockness Recycling reacondiciona a estudiantes de administracin agotados. El procesoutiliza una banda transportadora que lleva a cada estudiante por los cinco pasos del procesoe
Colorado Tech - ADMON - mpm
Universidad VirtualAdministracin de la Cadena de Valor2.5 Resolver problemas del captulo 6Profesor TitularDr. Alberto Rodrguez RodrguezCampusSedeEnero 19, 2011.Sante FeCoatzacoalcosProblema 2.- Rockness Recycling reacondiciona a estudiantes de a
Colorado Tech - ADMON - mpm
Universidad VirtualAdministracin de la Cadena de Valor2.5 Resolver problemas del captulo 6Profesor TitularDr. Alberto Rodrguez RodrguezCampusSedeEnero 19, 2011.Sante FeCoatzacoalcosProblema 2.- Rockness Recycling reacondiciona a estudiantes de a
Colorado Tech - ADMON - mpm
Universidad VirtualAdministracin de la Cadena de Valor2.4 Realizar reflexin tema SustentabilidadEQUIPO 37Olga Nora Garca Esquivel A00372979Tatiana Vanessa Mndez Martnez A01304717Amilcar Estrada Rodrguez A01304897Octavio Navarro Daz A01307499Alejan
Colorado Tech - ADMON - mpm
Universidad VirtualAdministracin de la Cadena de Valor2.5 Resolver problemas del captulo 6EQUIPO 37Olga Nora Garca Esquivel A00372979Tatiana Vanessa Mndez Martnez A01304717Amilcar Estrada Rodrguez A01304897Octavio Navarro Daz A01307499Alejandro Be
UCSD - CSE - 21
CSE 21: Homework 3October 12, 2009Problem 1In how many ways can 6 people be assigned to 4 nonempty teams?Problem 2An urn contains 5 red marbles and 6 white marbles.(a) How many ways can 4 marbles be drawn?(b) What if we must have 2 red marbles and
UCSD - CSE - 21
Name:Student ID:CSE 21Midterm #2 SolutionsNovember 17, 2009Each problem is worth 20 points. Show your work, especially on decision trees. Also, makesure you write legibly so that I have a chance of being able to read your solutions! Additionalscrat
UCSD - CSE - 21
Name:Student ID:CSE 21Practice Final ExamDecember 2, 20091. Dene the recurrence a(n + 2) = 4a(n + 1) a(n), , n 0, with a(0) = 1, a(1) = 2.(a) What is the value of a(5)?(b) Find an explicit closed form solution for a(n);(c) Prove by induction that
UCSD - CSE - 21
Solutions to the Practice Final ExamDecember 2, 20091. Solution:(a) a(0) = 1, a(1) = 2, a(2) = 7, a(3) = 26, a(4) = 97, and a(5) = 362.(b) Notice that the characteristic polynomial of the recurrence relation is x2 4x + 1, which has roots 2 3,nnyiel
UCSD - CSE - 21
CSE 21: Homework Solutions 2October 5, 2009Problem 1Teams A and B play in baseballs world series. Here, the team that rst wins four games wins the series.(a) What is the number of ways the series can occur?(b) What is the number of ways the series ca
UCSD - CSE - 21
CSE 21: Homework Solutions 3October 12, 2009Let S (n, k ) be the Stirling number of the second kind which counts thenumber of ways to partition n labeled elements into k disjoint, nonempty,unlabeled blocks.Problem 1In how many ways can 6 people be a
UCSD - CSE - 21
CSE21 FA11Homework #1 (9/26/11)1.1. An n-digit number is a list of n digits where the rst digit in the listis not zero (where we assume n 1).(a)How many n-digit numbers are there (as a function of n)?(b)How many n-digit numbers contain no 1s?(c)H
UCSD - CSE - 21
CSE21 FA11Homework #1 (9/26/11)1.1. An n-digit number is a list of n digits where the rst digit in the listis not zero (where we assume n 1).(a)How many n-digit numbers are there (as a function of n)?(b)How many n-digit numbers contain no 1s?(c)H
UCSD - CSE - 21
CSE21 FA11Homework #2 (10/3/11)In this homework, we will consider ordinary decks of playing cards whichhave 52 cards, with 13 of each of the four suits (Hearts, Spades, Diamondsand Clubs) with each suit have the 13 ranks (Ace, 2, 3, . . . , Jack, Quee
UCSD - CSE - 21
CSE21 FA11Homework #2 (10/3/11)In this homework, we will consider ordinary decks of playing cards whichhave 52 cards, with 13 of each of the four suits (Hearts, Spades, Diamondsand Clubs) with each suit have the 13 ranks (Ace, 2, 3, . . . , Jack, Quee
UCSD - CSE - 21
CSE21 FA11Homework #3 (10/10/11)3.1.Prove by induction thatnk=1k2 =n(n+1)(2n+1).63.2. It is desired to form three committees from a group of 3 men and 3women.(a) In how many ways can this be done?(b) Suppose that each of the committees must c
UCSD - CSE - 21
CSE21 FA11Homework #3 Solutions (10/15/11)3.1. Prove by induction thatnk2 =k=1n(n + 1)(2n + 1)6Sketch of proof. Step 1. We need to verify the base case for n = 1, i.e.1k=1=k=11 (1 + 1) (2 + 1).6Step 2. Proof by induction. We assume that n=1
UCSD - CSE - 21
CSE21 FA11Homework #4 (10/17/11)4.1.Prove by induction thatnk=1k3 = (nk=1k )2 .(Hint: First get an explicit form form the second sum. Then use induction.)4.2. (Note: This problem is fairly tough! Ill be impressed by anyone whocan get this one!
UCSD - CSE - 21
CSE21 FA11Homework #4 (10/17/11)4.1.Sketch of proof. Recall that we showed in class that n=1 k = n(n2+1) for allk22n 1. We will prove that by induction n=1 k 3 = n (n4+1) . We assume thatknn2 (n+1)23for some xed n 1. Note thatk=1 k =4n+1n
UCSD - CSE - 21
CSE21 FA11Homework #5 (10/24/11)5.1. (a) 10 cards are drawn at random one at a time with replacement froman ordinary deck of cards.What is the sample space? What is the probabilitythat no Ace appears on any of the draws? What is the probability that a
UCSD - CSE - 21
CSE21 FA11Homework #5 (10/17/11)5.1Solution. (a) The probability that no Ace appears on any of the drawsis ( 48 )10 . The probability that at least one King appears in 10 draws is521 ( 48 )10 . The probability that at least 2 Queens appear in the 10
UCSD - CSE - 21
CSE21 FA11Homework #6 (10/31/11)6.1. Five boys and three girls are throwing Frisbees. Each boy has oneFrisbee and throws it to a random girl. What is the probability that each ofthe girls gets at least one of thrown Frisbees?6.2. A box contains 20 li
UCSD - CSE - 21
CSE21 FA11Homework #6 (10/31/11)6.1. Five boys and three girls are throwing Frisbees. Each boy has oneFrisbee and throws it to a random girl. What is the probability that each ofthe girls gets at least one of thrown Frisbees?Answer: S (5, 3) 3!35=
UCSD - CSE - 21
CSE21 FA11Homework #7 (11/7/11)7.1. A bin contains 4 red balls, 5 white balls and 6 blue balls. A randomsubset S of 4 balls is removed (without replacement). Consider the following3 events:(1) E1 : S has exactly 2 red balls.;(2) E2 : S has balls of
UCSD - CSE - 21
CSE21 FA11Homework #7 Solutions7.1. A bin contains 4 red balls, 5 white balls and 6 blue balls. A randomsubset S of 4 balls is removed (without replacement). Consider the following3 events:(1) E1 : S has exactly 2 red balls.;(2) E2 : S has balls of
UCSD - CSE - 21
CSE21 FA11Homework #8 (11/14/11)8.1. An urn contains r red marbles and b blue marbles. A random marbleM1 is drawn out. If M1 is red, then it is put back into the urn along withc more blue marbles. On the other hand, if M1 is blue, then it is put back
UCSD - CSE - 21
CSE21 FA11Homework #8 (11/17/11)8.1Solution. Draw the decision tree. Then compute:(a)P r(M2 = red) =r+drbr+.r+b+cr+b r+b+dr+b(b)P r(M2 = red|M1 = red) =P r(M1 = blue|M2 = blue) =r.r+b+cbbr+b r+d+brb+cbb+ r+b r+d+br+d r+b+c8.2S
UCSD - CSE - 21
CSE21 FA11Homework #9 (11/22/11)9.1Does every connected graph has a spanning tree? Give either a proof or acounterexample.9.2(a) Select a spanning tree of minimum total weight from the following weightedgraph.(b) Find all spanning trees (list thei
UCSD - CSE - 21
CSE 21Midterm #1October 20, 20111. (a) How many rearrangements using all the letters of the wordSCHWARZENEGGER are there?Answer:14!3!2!2!= 36324288001.(b) How many rearrangements using only 13 of the letters of the wordSCHWARZENEGGER are there?
UCSD - CSE - 21
UCSD - CSE - 21
CSE 21 FA 11Practice Final Exam1. Dene the recurrence a(n + 2) = 4a(n + 1) a(n), , n 0, with a(0) = 1, a(1) = 2.(a) What is the value of a(5)?(b) Find an explicit closed form solution for a(n);(c) Prove by induction that the expression in (b) is vali
FAU - PHI - 2010
NelsonRobert NelsonProfessor Embree04/29/11PHI2010605ArtThere is a philosophy to art. There is a broad spectrum of what would be considered art anddifferent forms of art, even some that disprove another as art. Some questions that would beasked i