Math 30-440: Probability and Statistics Spring Semester 2008 Solutions to Homework 6 1. Problem 23b) (Ch 5): Here and everywhere Ill use Z for the standard normal. P (4 < X < 16) = P X 10 16 10 4 10 < < 6 6 6 = P (1 < Z < 1) = (1) (1) = 2(1) 1 = .6826.
2.
Prob & Stats SPRING 2008 Practice II Solutions
Problem 1. Let X and Y be continuous independent random variables, Y is uniformly distributed in [0, 1] and X has an exponential distribution with a parameter = 1. Find P (X + Y 1). Solution: X has density fX
Math 30-440: Probability and Statistics Spring Semester 2008 Exam 1 Solutions 1. (14 pts) A standard deck of cards contains 52 cards (4 suits, 13 denominations in each suit). A poker hand contains 5 cards. Assuming that all poker hands are equally likely,
Math 30-440: Probability and Statistics Spring Semester 2008 Exam 2 Solutions 1. (20 pts) a) A random sample of size 4 is taken from an unknown distribution, and the observed values are 2, 8, 0 and 6. Compute the sample mean and sample variance. Solution:
Probability and Statistics, Spring 2009 Practice II Solutions
Problem 1. Let X and Y be continuous independent random variables, Y is uniformly distributed in [0, 1] and X has an exponential distribution with a parameter = 1. Find P (X + Y 1). Solution: X
Math 30440 Probability and Statistics
Spring 2010 nal exam practice problems
Instructors: David Galvin and Daniel Cibotaru
1. At the end of the day in the amusement park you want to try out both the
white water rafting ride and the roller coaster. The tim
Answer Key for Exam A
1. Suppose the shoe size of men in South Bend is normally distributed with mean 10 and standard deviation of 2. What percentage of the population has a show size larger than 13? Let S N (10, 22 ). Thus
S-10 2
N (0, 1). S - 10 > 1.5 2
Math 30440 Probability and Statistics
Spring 2010 rst midterm exam, February 16 2010
Instructors: David Galvin and Daniel Cibotaru
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Name:
7Fh$ exanunaon contaum 7 probknns on 8 pages Onchuhng the xnm cover)
It is closedbook. You may use up to
MATH 30530
Introduction to Probability
November 16, 2011
Midterm Examination II Solutions
1. The joint probability mass function p(i, j) of the discrete random variables X and Y is given in
the table below.
Y
X
1
1 2/27
2 1/27
3 1/27
2
3
4/27 2/27
7/27 4/
Probability and Statistics Math 30440 SPRING 2009 Practice problems for the rst exam
Problem 1. A dodecahedron is a solid with 12 sides and is often used to display 12 months of the year. When this object is rolled, let the outcome be taken as the month a