 
Summary: Homework 1
Due Tuesday August 26
1. The probability density function of X is given by
f(x) =
10
x2 for x > 10
0 for x 10
(a) What is the cumulative distribution function of X?
(b) Compute P{12.5 X 14.5}
(c) Compute P{11.5 X 14.5, 12.5 X 15.0}
2. A gambler has in his pocket a fair coin and a two headed coin.
(a) He selects one of the coins at random, and when he flips it, it shows
heads. What is the probability that it is the fair coin?
(b) Suppose that he flips the same coin a second time and again it shows
heads. What is now the probability that it is the fair coin?
(c) Suppose that he flips the same coin a third time and it shows tails. What
is now the probability that it is the fair coin?
3. Let X be a random variable with cumulative distribution function given
in (1).
F(x) =
