MATH 180A Introduction to Probability Homework 2 (due 10/09/06)
1. After asking many individuals across the nation, a researcher comes with the following conclusion: 65% like dogs 55% like cats 25%
180A HW 3 Solutions
October 25, 2006
1) On a multiple-choice quiz with 3 possible answers for each of the 10 questions, what is the expected number of correct answers a student would get just by gues
MATH 180A Introduction to Probability Review for Midterm 1 (NOT due)
1. If 8 castles (i.e. rooks) are randomly placed on a chessboard, what are the chances that no rook can capture any of the others
180A HW 1 Solutions
October 4, 2006
1) A coin is tossed four times resulting in a sequence of heads and tails. Let A: exactly two heads B: heads and tails alternate C: first two tosses are headed. (a
MATH 180A Introduction to Probability Review for Midterm 2 (NOT due)
1. At the mayor election in a very large city, 51% of the people support candidate A, while 49% of the people support B. Use the n
180 Midterm 2 Review Solutions
1) At the mayoral election in a very large city, 51% of the people support candidate A, while 49% support B. Use the normal approximation to the binomial distribution to
180 Midterm 1 Review Solutions
October 10, 2006
1) If 8 castles (i.e. rooks) are randomly placed on a chessboard, what are the chances that no rook can capture any of the others? In other words, what
180 Final Solutions
December 4, 2006
1) Consider 0, 2 , f (x) = 91 x0 0<xa , a<x x2
What value(s) of a R make(s) f a probability density function? Answer Note that if f is a PDF
a
1 =
0
2 dx +
Math 180A - Homework 1; Solutions
1. (a) S = cfw_(x, y, i) : x = H, T ; y = H, T ; i = 1, ., 6.
(b) S = cfw_(H, H, i) : i = 1, ., 6.
(c) S = cfw_(x, y, i) : x = H, T ; y = H, T ; i = 1, 3, 5.
2. (a) C
Math 180A, Homework 3 Solution
October 18, 2017
1. Denote boy with b and girl with g. The combinations bg, bb, gb and gg all have equal probability
of 41 .
(a) Define B = cfw_second child is a girl =
Math 180A - Homework 2; Solutions
1. Problem 12 of Chapter 2.
S = cfw_ students in Spanish class., P (S) = 0.28.
F = cfw_ students in French class., P (F ) = 0.26.
G = cfw_ students in German class.,
180 Midterm 1 Solutions
October 17, 2006
1) Three dice are rolled. Let A: all numbers are even B: all numbers are equal C: there is at least one 6 Compute P (A B), P (B C), P (A B C ), and P (A B
MATH 180A Introduction to Probability Homework 6 (due 11/20/06)
1. Consider an urn with 1 red, 2 green and 3 blue balls. 5 balls are drawn from that urn without replacement. Let X be the number of r
180 HW 4 Solutions
1) Jimmy rides his old motorcycle every day of the year. The motorcycle starts with probability 1/2 each time Jimmy presses on the starter. Compute the probability that in a given
180A HW 5 Solutions
1) Suppose X has the uniform distribution on (0, 1). Compute the probability density function and expected value of: (a)X , where > 0 (b) log(X); (c)exp(X); (d) sin(2X) answer L
MATH 180A Introduction to Probability Homework 1 (due 10/02/06)
1. A coin is tossed four times. Let A: exactly two heads B: heads and tails alternate C: first two tosses are heads (a) Which events,
MATH 180A Introduction to Probability Homework 3 (due 10/25/06)
1. On a multiple-choice quiz with 3 possible answers for each of the 10 questions, what is the expected number of correct answers a st
MATH 180A Introduction to Probability Homework 4 (due 10/30/06)
1. Jimmy rides his old motorcycle every day of the year. The motorcycle starts with probability 1/2 each time Jimmy presses on the sta
MATH 180A Introduction to Probability Homework 5 (due 11/06/06)
1. Suppose X has the uniform distribution on (0, 1). Compute the probability density function and expected value of (a) X , where >
MATH 180A Introduction to Probability Homework 7 (due Wedenesday, 11/29/06)
1. Suppose X has the exponential distribution with parameter and Y has the exponential distribution with parameter . Assu
180A HW 6 Solutions
November 30, 2006
1) Suppose X has the exponential distribution with parameter and Y has the exponential distribution with parameter . Assume X and Y are independent. Let Z = X/(
MATH 180A Introduction to Probability Review for the Final (NOT due)
Please review homework sets 1-7, midterms 1 & 2, midterm reviews 1 & 2. The following problems focus on what was covered since mid
180A HW 6 Solutions
November 19, 2006
1) Consider an urn with 1 red, 2 green and 3 blue balls. 5 balls are drawn from that urn without replacement. Let X be the number of red balls picked and Y the n
Math 180A
Homework 2 Solutions
October 8, 2006
Problem 1
a) P (A B)C ) = 1 - P (A B) = 1 - (P (A) + P (B) - P (A C) = 1 - (.65 + .55 - .25) = .05 b) P (A B C ) + P (B AC ) = P (A) - P (A B) +