STAT610, Fall Semester of 2013
Assignment 5
(Deadline: 10/8/2013)
1. (Ex2.17) A median of a distribution is a value m such that P (X m)
(If X is continuous, m satises
m
f (x)dx
=
m f (x)dx
=
1
2 .)
1
2
1
and P (X m) 2 .
Find the median of the
following
STAT610, Fall Semester of 2013
Assignment 12
(Deadline: 11/26/2013)
1. (Ex5.21) What is the probability that the larger of two continuous iid random variables will
exceed the population median? Generalize this result to samples of size n.
2. (EX5.24) Let
STAT610, Fall Semester of 2013
Assignment 11
(Deadline: 11/19/2013)
1. (Ex5.8) Let X1 , . . . , X )n be a random sample, where X and S 2 are calculated in the usual
way. Show that
1
S=
2n(n 1)
n
n
2
(Xi Xj )2 .
i=1 j =1
Assume now that the Xi s have a nit
STAT610, Fall Semester of 2013
Assignment 10
(Deadline: 11/12/2013)
1. (EX4.54) Find the pdf of
n
i=1 Xi ,
where Xi s are independent uniform (0,1) random variables.
(Hint: Try to calculate the cdf, take logarithm, and recall the relationship between unif
STAT610, Fall Semester of 2013
Assignment 4
(Deadline: 10/1/2013)
1. (Ex2.2) In each of the following nd the pdf of Y .
(a) Y = X 2 and fX (x) = 1, 0 < x < 1.
(b) Y = eX and X has pdf
fX (x) =
1 (x/2 )/2
xe
,
2
0 < x < ,
2 a positive constant.
2. (Ex2.3)
STAT610, Fall Semester of 2013
Assignment 3
(Deadline: 09/24/2013)
1. (Ex1.47) Prove that the following functions are cdfs.
(a) (1 + ex )1 , x (, ).
(b) 1 ex , x (0, ).
2. (Ex1.51) An appliance store receives a shipment of 30 microwave ovens, 5 of which a
STAT610, Fall Semester of 2013
Assignment 2
(Deadline: 09/17/2013)
1. (Ex1.33) Suppose that 5% of men and .25% of women are color-blind. A person is chosen at
random and that person is color-blind. What is the probability that the person is male?
2. (Ex1.