Math 403 Fall 2009
Homework 3
Due Wednesday, September 16
WMMY: Ch 3 # 1,3,7*,9*,17*,19*,25,27*,29*,31*,71
* For these problems, sketch the PDF and CDF (if you found it), and
shade any areas under the PDF which correspond to probabilities you're
supposed to calculate.
Problem A: Consider an experiment where you roll two dice, and subtract the
smaller value from the larger value (or get 0 in case of a tie) to get a
random variable X.
a. What is the probability of getting 0?
b. What is the probability of getting 4?
c. Draw the probability distribution function for X.
Problem B: In an experiment where you roll two dice, let X be the random
variable which is the product of the two dice.
a. Make a table with possible values of X and their probabilities.
b. Draw the CDF for X.
Problem C: Recall that an ideal spinner has a uniform, continuous probability
distribution as shown on the left. If you spin twice and add the two
results, you get the continuous distribution shown on the right.
0.5 1
1
0.5 1 1.5 2
1
a. What is the probability that one spin is between .8 and 1?
b. What is the probability that one spin is not between .4 and .6?
c. What is the probability that the sum of two spins is less than 1?
d. What is the probability that the sum of two spins is more than 1.5?
e. What is the probability that the sum of two spins is between .5 and 1.5?