p(oxi3 dt5tt $ 'xertmxWtrx2 'ptdt d x 8 ! y ~ }| ) g y w) r 54%88$ 'r G{zxvuti sq n l i g ! po'mykjhfe xd85 t'yxw v DtrpigecaYX WUH S u sq T h f d b ` R V T R C A 9
Math/Stat 425, Solutions to Quiz #5
Problem # 2. Let X be the number of chips in a randomly selected chocolate chip
cookie. Assuming that X is a Poisson random variable with E [X ] = 5, compute the
pr
Math/Stat 425, Solutions to Quiz #6
Problem # 1. Let X be a continuous random variable with the probability density
function
x
2
if 0 < x < 2
f (x) =
0
otherwise
Let Y = X 2 . Find the cumulative dist
Math/Stat 425, Solutions to Quiz #6
Problem # 2. Let X be a continuous random variable with the probability density
function
1
x if 0 < x < 2
2
f (x) = 0 otherwise
f (x) =
Find the expected value E [X
Math/Stat 425, Solutions to Quiz #7
Problem # 1. Let X and Y be independent random variables uniformly distributed
on the unit interval [0, 1]. Compute P [Y < X + 0.5].
Solution: The density function
Math/Stat 425, Solutions to Quiz #7
Problem # 2. Let X and Y be independent random variables, having the joint probability density function
f (x, y ) = 4xy
if 0 < x < 1, and 0 < y < 1.
and f (x, y ) =
Math 425 / Stats 425
Homework 7
You must show all work when answering the questions. If the answer to the question is a calculation, be sure to write
down the formula you used or describe how you made
Math 425 / Stats 425
Homework 2
You must show all work when answering the questions. If the answer to the question is a
calculation, be sure to write down the formula you used or describe how you made
Math 425 / Stats 425
Homework 1
You must show all work when answering the questions. If the answer to the question is a
calculation, be sure to write down the formula you used or describe how you made
Math 425 / Stats 425
Homework 4
You must show all work when answering the questions. If the answer to the question is a calculation, be sure to write
down the formula you used or describe how you made
Math/Stat 425, Solutions to Quiz #5
Problem # 1. A fair die is rolled 10 times. What is the probability that a 6 comes
up at least three times? [Answer can be expressed using factorials, sums. State w
Math/Stat 425, Solutions to Quiz #4
Problem # 2. Six people check their coats, and then coats are handed back at random
so that each person gets precisely one coat. Let X be the number of people who g
Solutions - Homework #3
1
1.1
Chapter 2
Problems
1. Problem 17: If 8 castles (rooks) are randomly placed on a chessboard, compute the probability that none of the rooks can capture any of the other
Math/Stat 425, Solutions to Quiz #1
Problem # 1. We are given a 5 5 square grid with vertices A = (0, 0), B = (3, 2),
and C = (5, 5) marked. We want to count paths between these points that move only
Math/Stat 425, Solutions to Quiz #1
Problem # 2. Consider a group of 9 dierent people. Two committees are to be
formed, one of four people and one of three people. (No person can serve on both committ
Math/Stat 425, Solutions to Quiz #2
Problem # 1. For two events A and B in a probability space S, we have
3
P (A) = P (B ) = .
4
(a) Suppose we know that P (A B ) = 5 . What is P (AB )?
6
(b) Suppose
Math/Stat 425, Solutions to Quiz #2
Problem # 2. A student must choose exactly two of three electives: Art, Business, or
Communications. The student chooses Art with probability 5/8, Business with pro
Math/Stat 425: Solutions to Quiz 3
Problem # 1. There is a box containing 9 red balls and 18 blue balls.
Suppose that one draws 6 balls at random from the box (without replacement). What is the probab
Math/Stat 425: Solutions to Quiz 3
Problem # 2. A fair coin is tossed three times. What is the probability
that the coin shows heads on the second toss, given that it showed heads
exactly twice?
Solut
Math/Stat 425, Solutions to Quiz #4
Problem # 1. A box contains 3 red marbles and 2 green marbles. Suppose that one
picks 3 marbles randomly without replacement from the box. Let X count the number of
Math 425 / Stats 425
Homework 3
You must show all work when answering the questions. If the answer to the question is a
calculation, be sure to write down the formula you used or describe how you made