EE 131A Probabilities Instructor: Vwani Roychowdhury
Problem Set #1 Wednesday, October 5, 2005 Due: Wednesday, October 12, 2005
1. Problem 2.4
2. Problem 2.7
3. Problem 2.24
4. Problem 2.21, Use probability axioms and corollaries.
5. Problem 2.27
6. Probl
EE 131A Probability Instructor: Vwani Roychowdhury
Midterm Solution Fall 2005
1. (a) P [A B] = P [A|B]P [B] = 0.1 P [A B] = 0.8 = P [A] + 0.2 - 0.1 P [A] = 0.7
(b) Since P [A|B] = P [A], they are NOT independent. P [A B] = 0, hence they are NOT mutually e
EE 131A Probabilities Instructor: Vwani Roychowdhury
Midterm Practice Problem Set Fall 2005
Problems 1 through 4 comprised the midterm exam for Fall 2004. 1. (30 pts) A box contains 3 distinct dice. Die #1 is a fair die. Die #2 lands on 1 with probability
EE 131A Probabilities Instructor: Vwani Roychowdhury
Practice Problem Solution Set II
1. Problem 3.153 (a) Pr[pass the test] = (1 - p) + p(1 - ) Pr[fail the test] = p Pr[k items] = [(1 - p) + p(1 - )]k-1 p (b) The answer is (c) The answer is 2. Problem 3.
EE 131A Probabilities Instructor: Vwani Roychowdhury
Practice Problem Set
1. Problem 3.153 2. Problem 3.156 3. Problem 3.58 4. Problem 3.91 5. Problem 3.89 6. Problem 5.26 7. Problem 5.28 8. Problem 4.13 9. Problem 4.17
1
EE 131A Probability Instructor: Vwani Roychowdhury
Problem Set #6 Wednesday, November 16, 2005 Due: Wednesday, November 23, 2005
1. Problem 3.46 2. Problem 3.47 3. If X is a normal random variable with parameters = 3 and 2 = 9, find (a) P [2 < X < 5], (b)
EE 131A Probabilities Instructor: Vwani Roychowdhury
Problem Set #5
1. Problem 3.4.
(a) SY = [0, 1). (b) It's a circle (as well as its inside area) with its center at the origin, its radius as y. (c) P [Y y] = 2. Problem 3.15 (a) X is a r.v. of mixed type
EE 131A Probabilities Instructor: Vwani Roychowdhury
Problem Set #5 Wednesday, November 9, 2005 Due: Wednesday, November 17, 2005
1. Problem 3.4 2. Problem 3.14 3. Problem 3.15 (b) 4. Problem 3.17 5. Problem 3.23 6. Problem 3.27 7. Problem 3.33 8. Problem
EE 131A Probabilities Instructor: Vwani Roychowdhury
Problem Set #4
1. Problem 2.42 We assume (reasonably) that each time we try to catch an animal this is as likely to be caught as any of the remaining uncaught animals. The number of ways we can capture
EE 131A Probabilities Instructor: Vwani Roychowdhury
Problem Set #4 Wednesday, October 26, 2005 Due: Wednesday, November 02, 2005
1. Problem 2.42. 2. Problem 2.45. 3. Problem 2.93. 4. A football team consists of 20 black and 20 white players. The players
EE 131A Probabilities Instructor: Vwani Roychowdhury
Problem Set #3: Solutions
1. The amount of time cars are parked in a parking lot follows an exponential probability law with average time of 1 hour. The charge for the parking is $1 for each half-hour o
EE 131A Probabilities Instructor: Vwani Roychowdhury
Problem Set #3 October 21, 2005 Due: October 28, 2005
1. The amount of time cars are parked in a parking lot follows an exponential probability law with average time of 1 hour. The charge for the parkin
EE 131A Probabilities Instructor: Vwani Roychowdhury
Problem Set #2
1. Problem 2.57. Let X denote the input and Y the output. (a) P [Y = 0] = P [Y = 0|X = 0]P [X = 0] + P [Y = 0|X = 1]P [X = 1] = 0.5(1 - (b) P [X = 0|Y = 1] = = P [Y = 1|X = 0]P [X = 0] P
EE 131A Probabilities Instructor: Vwani Roychowdhury
Problem Set #2 Wednesday, October 12, 2005 Due: Wednesday, October 19, 2005
1. Problem 2.57
2. Problem 2.59
3. Problem 2.61
4. A familily has two children, assuming that one of them is a girl what is th
EE 131A Probabilities Instructor: Vwani Roychowdhury
Problem Set #1: Solutions
1. Problem 2.4 (a) S = cfw_(i, j), 1 i 6, 1 i i. (b) A = cfw_(4, j), 1 j 4. (c) A = cfw_(i, 3), 3 i 6. (d) A = cfw_(6, 6).
2. Problem 2.7 (a) S = cfw_(1,2,3), (1,3,2), (2,1,3),
EE 131A Probabilities Instructor: Vwani Roychowdhury
Practice Problems Solutions Fall 2005
1.
m
P [nth is new] =
i=1 m
P [nth is new|nth = i]pi P [i is not in the f irst (n - 1)]pi
i=1 m
= =
i=1
[(1 - pi )]n-1 pi
(a) Let define: A1 = A is hit and A0 = A i