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Unformatted text preview: um onday, Feb. 07 in the lecture ﬁlerSotuhons misﬁt—m 3 IMPORTANT NOTES: 1. You MUST write your ’I\1torial Section (it is either A1 or A2 or A3 or A4).
2. Work independently (do not work in groups with other student(s)).
3. You MUST show your work for each question. Due: 4. Assignments will n_ot be accepted after the due time and date (in fact the solutions will be
posted soon after the due time and date). 5. Answer each question in the space provided (use extra pages if needed) AND staple all
your pages together before submitting the assignment. Questions 1. marks] An urn contains :3 red and 3 blue chips. Suppose that 4 of these chips are selected
at random and transferred to a second urn. which was originally empty. If a randomly selected chip from
this second urn is blue. what is the probability that :2 red and 2 blue chips were transferred from the first urn to the second urn? Lac
8 7 ‘l'lrte. randomla §€\€C\’€6l Cw? Aerom Urh‘#2 i? E‘EE A 2. LI. recl dud O blM JAWS we’ve *mmsﬁevmd
L§ A3 =3 ’/ // ’/ // 1/ I,
A; = Z ’/ ’/ Z " ”' ” ’/
Al :2 l J I, 3 ’7 '1 0 //
P (RABX —, PCBW‘Q PUS‘P'» , wluuu; STAT 3502 A Assignment#1 Questions 2. [5 ma.rks.f Let k 2 3 be any given integer. What is the probability that a random kdigit
number will have at least one 0. at least one 1. and at least one ‘2? (Note: as usual. every number starts
with either a 1. or a 2. or a 9 (but not a 0).) . , si—
Since W \ we “0“”? Lﬁlhowtl K°‘*'a*“”m‘0€m Mow/ A r. We selec‘lecl number has all 002 O akaML Carmai’loe a Zero] AMWV = PCAAB (\c\ r; \— P010 B’UC’) Bil, PtA’UB'UC’ )s PtA’)+ Pte’l + P (c’)
Pux’ne’>P(A’<\C’)WM)
+ P (A’n B’nc’l c: . 4 K
a“ one?“ mm“ 3 <3
3"" ‘ + \41 + ﬂ  ' pm
(0)(IOK') (MOO 5 Law”) \ L‘IlQo )
<5“ (7)66“ + 7“ .. ~———MO¥\ " (q)(\0t<\) (q)C\OK\\ . STAT 3502 A Assignment#1 Questions 3. ['3 marks./' The cumulative distribution function (cdf) of a random variable X is given by:
F(I):0if1<731 F(I):3/8if—3SI<0: F(I): 1/2ifOSI<3: F(I)=3/4if3§I<1. and
17(1) : 1 if .r 2 4. Compute VLX') and E(X (Hint: First ﬁnd the probability mass function of X.) STAT 3502 A Questions 4. ['3 marks}; Suppose that n integers are randomly selected from {1. 2.   Let X be the largest number selected. Find E(.\')r Assigmnent#1  ‘ N} with replacement. STAT 3502 A Assignment# 1 Questions 5. Short questions: 5(a). [3 marks._/ Suppose that independent Bernoulli trials with parameter p are performed successively. Let N be the number of trials needed to get .r successes, and X be the number of successes in the ﬁrst n
trials. Show that P(N 2 n) = f P(X : 1). mm A P W)
WW3 9c r‘bﬂ U! STAT 3502 A Assignment#1 5(b). [3 marksf Let the random variable X have a Poisson distribution with parameter A. Show that for
every n 21 one has ELY") : AE((X ~1)"‘1). Note that. using this formula. we can ﬁnd E(X).E(X2).
recursively. ...
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This note was uploaded on 02/15/2011 for the course SYSC 3600 taught by Professor Adsd during the Spring '10 term at Universidad Alfonso X El Sabio.
 Spring '10
 adsd

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