Probability

For Summer 2019 class: please ignore the homework due dates below. However, these are the homework problems you should work. Homework will not be collected, but it is strongly suggested you do these problems.

Aug. 27- Section 2.3, #s 4, 5, 6, 7

Aug. 29 - Sections 2.4 and 2.5, #s 11, 14, 15, 18, 21, 22, 23, 27, 29, 33

Sept. 3 - Section 2.6, #s 35, 36, 41, 43, 46, 47, 51, 53, 57, 58, 68, 69

Sept. 5 - Section 2.7, #s 71, 75, 77, 81, 83. Section 2.8, #s 84, 86, 89, 97, 99, 104

Sept. 8- Section 2.9, #s 114, 115, 119, 120, 121, Section 2.10, #s 128, 132, 135, 137

Sept. 10 - Section 3.2, #s 2, 4, 6, 10, Section 3.3, #s 19, 23, 27, 29, 32, 33

Sept. 12 - Section 3.4, #s 40, 44, 48, 51, 56, 57, 65

Sept. 15 - Section 3.5, #s 66, 67, 70, 72, 77, 80, 85

Sept. 17 - Section 3.6, #s 90, 91, 93, 94, 97, Section 3.7, #s 102, 105, 110

Sept. 19 - Section 3.8, #s 122, 130, 134, 138, 141,

Sept. 22 - Section 3.9, #s 147, 148, 150, 151, 153, 159, 160, Section 3.11, #s 167, 168

Sept. 24 - Exam I Review - Also, Section 4.2, #s 8, 9, 15, 17, Section 4.3, #s 21, 25, 26, 32, 34, 35

Sept. 26 - Exam I (covers Chapters 2 and 3)

Sept. 29 - No homework due!

Oct. 1 - Section 4.4, #s 39, 41, 42, 43, 45, 50,

Oct. 3 - Section 4.5, #s 58, 59, 61, 62, 71, 75

Oct. 6 - Section 4.6, #s 81, 82, 89, 92, 94, 95, 104, 109, 112

and the following:

1. The times between arrivals to the YMCA are independent exponential random variables with mean 3 minutes.

(a) What is the probability that the time between the 4th and 5th customers exceeds 5 minutes?

(b) Given the 4th customer arrived 10 minutes ago, what is the probability that the time from now until the next arrival exceeds 5 minutes?

(d) The 6th customer just arrived. What is the distribution of time until the 11th customer arrives, and what is the expected amount of time until this happens?

2. Prove that the geometric random variable has the memoryless property (in fact, it's the only discrete rv. that does, but you don't have to prove uniqueness).

Oct. 8 - Section 4.7, #s 124, 125, 128, 130

Oct. 10 - Section 3.9, #158, Section 4. 9, # 137, 139, 140, 141, 143, 144, 145, Section 4.10, #s 146, 149

Oct. 13 - No classes. Fall break!

Oct. 15 - Section 4.11, #s 155, 156, 157, 159

Oct. 17 - HA! No homework due.

Oct. 20 - Section 5.2, #s 7, 9, 11, 15, 17

Oct. 22 - Section 5.3, #s 19, 23, 25, 34, 36

Oct. 24 - Section 5.4, #s 43, 45, 48, 57, 61, 64, 70, 71

Oct. 27 - Sections 5.5 and 5.6, #s 75, 77, 79, 81

Oct. 29 - Section 5.7, #s 89, 91, 93, 94, 96, 98

Oct. 31 - Section 5.8, #s 103, 105, 107, 108, 110

Nov. 3 - Section 5.9, #s 119, 123, 124, 126

Nov. 5 - Exam II Review. Also, Section 5.11, #s 133, 136, 139, 140, 142

Nov. 7 - Exam II (covers Chapters 4 and 5).

Nov. 10 - Section 6.3, #s 1, 3, 7, 8, 14, 22

Nov. 12 - Section 6.4, #s 23, 28, 29, 30

Nov. 14 - No Homework Due! But the next one is long!

Nov. 17 - Section 6.5, #s 37, 38, 40, 41, 42, 43, 49, 52, 54, 57, and the following: Suppose X is distributed geometric(p). How does the random variable pX/lambda behave as p goes to 0? Here, lambda is a constant. Hint: Use moment generating functions.

Nov. 19 - Section 6.7, #s 72, 74, 76, 81

Nov. 21 - No homework due!

Nov. 24 - Exam III Review. Section 7.2, #s 11, 12, 14, 15, 20, 21, 33, 34, 35

Nov. 26 - No classes- Thanksgiving break.

Nov. 28 - No classes - Thanksgiving break.

Dec. 1 - Exam III (covers Chapters 6 and 7). Also, Section 7.3, #s 43, 44, 46, 47, 52, and the following:

The average and standard deviation of railroad cars and their contents are 8,000 lbs and 1,000 lbs, respectively. Fifty of these cars are to be loaded onto a barge. What is the approximate chance that the total weight exceeds the load capacity of the barge of 425,000 lbs?

Dec. 3 - Final Exam Review. Final exam is cumulative.

Dec. 5 - Final Exam. 8:00 am - 10:00 am.