Statistics 116 - Fall 2004
Theory of Probability
Assignment # 4
Due Monday, October 25
show (and briefly explain) all of
your work
Q. 1) (Ross #3.60) A true-false question is to be posed to a husband and a wife
team on a quiz show. Both the husband and th
Statistics 116 Fall 2004
Theory of Probability
Assignment # 8
Solution
Q. 1) (Ross # 6.39) Choose a number at random from the set of numbers
{1, 2, 3, 4, 5}. Now choose a number at random from the subset {17 . . . 7X}.
Call this second number Y.
(a) Find
Statistics 116 Fall 2004
Theory of Probability
Assignment # 9
SOLUTIONS
Q. 1) (Ross # 7.51) The joint density of X and Y is given by
0<m<y,0<y<oo
otherwise.
1;, = y
f( y) {0
Compute E[X3|Y :
Solution:
Since fX|Y(<1?|Z/) =
0
2/31 _ 3
0:1: yd$y/4.
(a) I
Statistics 116 Fall 2004
Theory of Probability
Assignment # 6
Q. 1) (Ross #5.19) Let X be a normal random variable with mean 12 and
variance 4. Find the value of c such that P(X > c) = 0.10.
Answer: Letting Z = (:1: 12)/2 then Z is a standard normal.
Q- 1)
Q- 2)
Statistics 116 Fall 2004
Theory of Probability
Assignment # 2
(Ross #1.8 - Theoretical) Prove that
m
("T") = (Z><T)+(T>(._1)+-~-+(Z)(Zf>-
HINT: Consider a group of n men and m women. How many groups of
size 7" are possible?
Solution:
T
Statistics 116 - Fall 2004
Theory of Probability
Assignment # 7
Due Friday, November 12
show (and briefly explain) all of
your work
Q. 1) (Ross # 6.2) Suppose that 3 balls are chosen without replacement from
an urn consisting of 5 white and 8 red balls. L