Math 30-440: Probability and Statistics
Spring Semester 2008
Solutions to Homework 4
1. Problem 40: If the expectation is 2, and the random variable takes on only values 1, 2 and
3, then the way to make the variance small is to make the rv always take val
Math 30440 Probability and Statistics
Spring 2010 second mid-term exam practice problems 2
Instructors: David Galvin and Daniel Cibotaru
1. The time until the next large earthquake (magnitude greater than 4.8) occurs
in the United States is an exponential
Math 30440 Probability and Statistics
Spring 2010 second mid-term exam practice problems
Instructors: David Galvin and Daniel Cibotaru
1. Let X and Y be continuous independent random variables, with X uniformly
distributed on [0, 1] and Y exponentially di
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:
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,
Prob & Stats SPRING 2008
Practice I
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 appearing on the upper face. Also let
A = cfw_Janu
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
Prob & Stats SPRING 2008
Practice II
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).
Problem 2.
One-tenth of 1% of a cert
Math 30440 Probability and Statistics
Spring 2010 rst mid-term exam practice problems
Instructors: David Galvin and Daniel Cibotaru
1. A random variable X is given by density function
c
x4
f ( x) =
0
if x 4
if x < 4
(a) Find c.
(b) Calculate the expectati