Statistics 265
Elements of Probability Theory
Fall Term 2000
Assignment 6
Due: Tuesday December 5, 2000
Solutions
6.2 Let Y be a random variable with a density function given by
(3 2
;1 y 1
f (y) = 2 y
0
otherwise.
a. Find the density function of U1 = 3Y:
Statistics 265
Elements of Probability Theory
Fall Term 2000
Assignment 1
Due: Friday September 15, 2000
Solutions
1.5 The following results on summations will help us in calculating the sample variance s2 : For any constant
cn
P
a. c = nc:
b.
c.
i=1
n
P
Statistics 265
Elements of Probability Theory
Fall Term 2000
Assignment 2
Due Friday September 29, 2000
Solutions
2.52 In the de nition of the independence of two events, you were given three equalities to check: P (A j B ) =
P (A) or P (B j A) = P (B ) o
Statistics 265
Elements of Probability Theory
Fall Term 2000
Assignment 3
Due : Friday October 27, 2000
Solutions
3.40 A particular concentration of a chemical found in polluted water has been found to be lethal to 20% of
the sh that are exposed to the co
Statistics 265
Elements of Probability Theory
Fall Term 2000
Assignment 4
Due: Friday November 10, 2000
Solutions
4.2 Consider a random variable with a geometric distribution (Section 3.5), that is,
p(y) = qy;1p:
y = 1 2 3 : :
0 < p < 1:
a. Show that Y ha
Statistics 265
Elements of Probability Theory
Fall Term 2000
Assignment 5
Due: Tuesday December 5, 2000
Solutions
5.94 A target for a bomb is in the center of a circle with radius 1 mile. A bomb falls at a randomly selected
1
point inside that circle. If