Assignment #1 (Due Monday, September 16):
Section 1.2: Problems: 7, 8, 9, 10, 16, 17ab, 18, 19, 20, 21, 22, 23, 26
(Not assigned, but very interesting: Section 1.2: Problems 24, 25, 31)
Additional problems:
A1.1: Two fair dice are rolled. Determine the probability that twice one of the numbers obtained is less than the other number obtained.
A1.2: A square dartboard has the largest possible circle inscribed in it. We throw a dart 100,000 times. Suppose the dart hit the square dartboard outside of the circle 21,776 times while all the remaining hits were inside the circle. Estimate the value of pi. (Assume the probability of hitting any point is the same and that each time we hit the dartboard.)

Assignment #2 (Due Monday, September 23):
Part 1:
Section 2.2: Problems 1 through 8a-f, 14a, 15
(Not required but interesting: Section 2.2: Problems 12, 16)
Part 2 of the assignment will be assigned in class on a separate sheet.

Assignment #3 (Due Monday, September 30, in class):
Section 3.1: 5, 6, 8, 10, 11, 13, 15, 17
Section 3.2: 7, 8, 9, 10, 11 (such a cool problem!), 12de, 13, 21 , 22, 25, 39
(Not assigned, but interesting): 3.2: 18, 35

Assignment #4 (Due Wednesday, October 9, in class):
Section 4.1: 5, 10, 12, 15, 16, 17, 18, 22, 23, 24, 38, 39, 46
Section 4.2: 2, 4, 5, 7, 8, 9

Assignment #5 (Due Friday, October 18, in class):
Section 5.1: 7, 8, 9, 14, 16, 17, 18, 19, 21, 23, 24, 28, 29, 40
Section 5.2: 1, 2, 5, 9, 13, 14, 19, 20

Assignment #6 (Due Wednesday, October 30, in class):
Section 6.1: 4, 5, 6, 8, 13, 14, 17, 18, 19, 23
Section 6.2: 4, 7, 9, 11, 12
Section 6.3: 2, 3, 4ab, 6a, 8, 9, 10

Assignment #7 (Due Friday, November 8, in class):
Section 7.1: 1, 2, 3, 5, 6, 10 (The proof is constructive: show what to do to get the desired result)
Section 7.2: 1, 2ab, 3ab, 4, 5a, 9, 10, 12

Additional Problems for Assignment 7:
Problem 7.A:
The densities of random variables X and Y are as follows:
f(x) = { 1/2 for 0<=x<=2; 0 elsewhere }, and g(y) = { 1 for 0<=y<=1; 0 elsewhere}.
Find density h(z) of random variable Z = X + Y.

Problem 7.B:
The densities of random variables X and Y are as follows:
f(x) = { x/2 for 0<=x<=2; 0 elsewhere}, and g(y) = { y/2 for 0<=y<=2; 0 elsewhere}.
Find density h(z) of random variable Z = X + Y.

Assignment #8 (Due Monday, November 18, in class):
Section 8.1: 1, 4, 5, 6, 7, 8 (show work!), 10, 12 (Hint: show that p of the complement approaches 0 and use Chebyshev inequality)
Section 8.2: 3 (graph just a few points), 4, 5, 6 (show the results of comparison), 7, 8, 9, 10, 11, 12, 13

Assignment #9 (Due Monday, December 2, in class):
Section 9.1: 1, 2, 3, 4, 6, 10, 12, 13
Section 9.2: 2, 3, 5, 6, 9
Section 9.3: 1, 2, 11
Section 10.1: 1 (only g(t), no h(z)!), 3 (only parts b and c, without using part a), 5 (only MGF for part b), 7

Assignment #10 (Due Monday, December 16; please slide it under my door, if I am not in the office):
Section 10.3: 1, 2, 3, 4, 5, 7, 8, 9
Additional Problems:
Problem 10.A:
Two fair coins are tossed. Let X be the number of heads and let Y be the number of tails.
Find covariance Cov(X, Y), and the coefficient of correlation.
Problems 10.B and 10.C will be handed in class on Friday, 12/6.