Mathematics 4255
Midterm 2
March 31, 2011
Partial credit will be awarded for your answers, so it is to your advantage to explain your
reasoning and what theorems you are using when you write your solutions. Please answer
the questions in the space provide
Mathematics 4255
Final
May 7th 2013
Partial credit will be awarded for your answers, so it is to your advantage to explain your
reasoning and what theorems you are using when you write your solutions. Please answer
the questions in the space provided and
Mathematics 4255
Midterm 1 with solutions
February 19, 2013
Partial credit will be awarded for your answers, so it is to your advantage to explain your
reasoning and what theorems you are using when you write your solutions. Please answer
the questions in
Mathematics 4255
Midterm 1
February 19, 2013
Partial credit will be awarded for your answers, so it is to your advantage to explain your
reasoning and what theorems you are using when you write your solutions. Please answer
the questions in the space prov
Mathematics 4255
Midterm 2 with solutions
April 2nd 2013
Partial credit will be awarded for your answers, so it is to your advantage to explain your
reasoning and what theorems you are using when you write your solutions. Please answer
the questions in th
Mathematics 4255
Midterm 2
April 2nd 2013
Partial credit will be awarded for your answers, so it is to your advantage to explain your
reasoning and what theorems you are using when you write your solutions. Please answer
the questions in the space provide
Mathematics 4255/5255
Final exam with solutions
May 3rd, 2011
Partial credit will be awarded for your answers, so it is to your advantage to explain your
reasoning and what theorems you are using when you write your solutions. Please answer
the questions
Math 4255
Spring 2011
Solutions for Take-Home Assignment # 1
1. Solution of ex5 pp50:
The sample space is given by
S = cfw_(1 , 2 , 3 , 4 , 5 ), i = 0, 1, i = 1, . . . , 5 .
(a) Hence the number of outcomes in the sample space is 2 2 2 2 2 = 25 = 32.
(b)
Math 4255
Spring 2011
Solutions for Take-Home Assignment # 4
1. Solution of 4.17 pp 175:
(a) P (X = i) = F (i) limbi F (b) hence
P (X = 1) = F (1) lim F (b)
b1
1 11
b
+
lim b 1
2
4
4
11
1
=.
24
4
=
Do the same for i = 2, 3.
(b)
P (1/2 < X < 3/2) =
lim
b(
Math 4255
Spring 2011
Solutions for Take-Home Assignment # 5
1. Solution of 5.2 pp224:
(a) f is a density function if f 0 and if
by parts
f (x)dx = 1. Now, using an integration
xe
x/2
dx =
2xex/2 |
0
ex/2 dx
+2
0
0
=
4ex/2 |
0
= 4.
Hence C = 1/4.
(b) Usin
Math 4255
Spring 2011
Solutions for Take-Home Assignment # 6
1. Solution of 5.13 pp225:
X is a uniform R.V on (0,30) hence its density function is given by
f (x) =
1
30
if x (0, 30),
otherwise
0
And its distribution function is given by
if x 0,
0
x
if x (
Math 4255
Spring 2011
Solutions for Take-Home Assignment # 7
1. Solution of 6.10 pp287:
(a) Let C = cfw_(x, y ) R2 , x < y . Hence,
P (X < Y ) = P (X, Y ) C )
=
f (x, y )dxdy
C
y
e(x+y) dxdy
=
0
0
=
y
e
ex dx dy
y
0
0
ey ex |y dy
0
=
0
ey 1 ey dy
=
0
1
=
Mathematics 4255
Midterm 1 with solutions
February 22, 2011
Partial credit will be awarded for your answers, so it is to your advantage to explain your
reasoning and what theorems you are using when you write your solutions. Please answer
the questions in
Mathematics 4255
Midterm 1
February 22, 2011
Partial credit will be awarded for your answers, so it is to your advantage to explain your
reasoning and what theorems you are using when you write your solutions. Please answer
the questions in the space prov
Mathematics 4255
Midterm 2 with solutions
March 31, 2011
Partial credit will be awarded for your answers, so it is to your advantage to explain your
reasoning and what theorems you are using when you write your solutions. Please answer
the questions in th
Mathematics 4255
Final with solutions
May 7th 2013
Partial credit will be awarded for your answers, so it is to your advantage to explain your
reasoning and what theorems you are using when you write your solutions. Please answer
the questions in the spac