MTH 451 Summer 2013
Problem Set 11
1. If the joint pdf of two random variables X and Y is given by
f (x, y ) =
1
(2x
4
0
+ y ) for 0 < x < 1, 0 < y < 2
elsewhere
(a) Find cov(X, Y )
(b) Find the condi
MTH 451 Summer 2013
Problem Set 9
1. If the pdf of a random variable X is given by
x
2
1
f (x) =
2
3x
2
0
for 0 < x < 1
1<x2
2<x<3
elsewhere
Find the expected value of g (X ) = X 2 5X + 3
2. If the j
MTH 451 Summer 2013
Problem Set 10
1. If the pdf of a random variable X is given by
f ( x) =
Find , 2 and variance of X .
x
2
for 0 < x < 2
0 elsewhere
MTH 451 Summer 2013
Problem Set 12
1. Find the MGF for the uniform discrete distribution. (Note: You will need the formula
for sum of a geometric series with nite terms to complete this).
2. A biased
MTH 451 Summer 2013
Problem Set 12
1. The MGF of the geometric distribution is given by (without proof)
MX (t) =
et
.
1 et (1 )
Use dierentiation to show that (convincingly) the mean =
1
. (Please sho
MTH 451 Summer 2013
Problem Set 1
Name:
1. In a group of 10 people each person has a dierent birthday. How many dierent arrangements of these birthdays are there (assuming each year has 365 days)?
2.
MTH 451 Summer 2013
Problem Set 6
1. The pdf of a random variable X is given by
f (x) =
k
x
0
for 0 < x < 4
elsewhere
(a) Find k
(b) Find P (X < 1 ) and P (X > 1)
4
(c) Find the corresponding distribu
MTH 451 Summer 2013
Problem Set 5
1. Find the distribution function of the random variable that has the probability distribution for x = 1, 2, 3, 4, 5
x
f (x) =
15
2. Find the value of c so that the f
MTH 451 Summer 2013
Problem Set 4
1. In a recent political survey of 200 people in Texas, 120 people approve Presidents second term, 40 said they dont approve and 40 said they dont care. Among these t
MTH 451 Summer 2013
Problem Set 2
Note: You do not have to nd numerical values of permutations and combinations.
1. In class we calculated the probability of getting a full house in a poker game. Anot
MTH 451 Summer 2013
Problem Set 3
1. A bicycle company manufactures its product in two plants X and Y. Plant X manufactures 60% of the bicycles. 4% of the bikes from X and 5% of the bikes from Y are
d
MTH 451 Summer 2013
Problem Set 7
1. Find the value of k such that the joint pdf of two random variables X and Y is given by
f (x, y ) =
k x(x y ) for 0 < x < 1, x < y < x
0
elsewhere
2. If the joint
MTH 451 Summer 2013
Problem Set 8
1. If the joint pdf of two random variables X and Y is given by
f (x, y ) =
1
(2x
4
+ y ) for 0 < x < 1, 0 < y < 2
elsewhere
0
(a) Find the marginal density of X
(b)