M 362K, Spring 03, Smith
Assignment for Friday, December 5
To Hand In:
1. p. 294 #41(a)
2. The joint probability density function of continuous random variables
X and Y is
2 if 0 < x <
y < 1
f(x,y) =
0 otherwise.
Find the conditional pdf fX|Y(x|y).
3. A certain elevator can hold 2700 pounds safely. The weight of a random
athlete has a normal distribution with mean 225 pounds with standard deviation
25 pounds. What is the probability that the elevator can safely carry
12 randomly chosen athletes? [Hint: The weight of the ith athlete
is a random variable Xi. The random variables X1, X2,
... , X12 are independent and identically distributed.]
4. One type of lightbulb has lifetime (in months) which is an exponential
random variable with parameter 0.1. A second type of lightbulb has lifetime
(in months) which is an exponential random variable with parameter 0.5. If
you randomly choose a lightbulb of the first type, use it until it burns out,
then replace it with a randomly chosen lightbulb of the second type, what
is the expected time until both bulbs have burned out?
5. The radius of a cylinder is a random variable uniformly distributed on
(0,1). The height of the cylinder is uniformly distributed on (0,2). Find
the expected value of the volume of the cylinder. (Added 11/28/03): Assume
the height and radius are independent random variables.