MATH/STAT 3360, Probability
FALL 2014
Toby Kenney
Homework Sheet 2
Model Solutions
Basic Questions
1. What is the probability that a ve-card poker hand is a three of a kind
(three cards of one rank, two cards of dierent ranks, which are not the
same rank
MATH/STAT 3360, Probability
FALL 2014
Toby Kenney
Homework Sheet 1
Model Solutions
Basic Questions
1. A statistics course has 8 homework sheets. Each homework sheet has 7
questions, and each question has 3 parts. How many part-questions are
there in total
MATH/STAT 3360, Probability
FALL 2012
Toby Kenney
Homework Sheet 2
Model Solutions
Basic Questions
1. For an experiment with sample space cfw_1, 2, 3, 4, 5, is there a probability
P such that P (cfw_1, 2, 3) = 0.4, P (cfw_1, 3, 4) = 0.6 and P (cfw_2, 4, 5
MATH/STAT 3360, Probability
FALL 2012
Toby Kenney
Homework Sheet 7
Model Solutions
Basic Questions
1. If X is exponentially distributed with parameter and Y is uniformly
distributed on the interval [a, b], what is the moment generating function
of X + 2Y
MATH/STAT 3360, Probability
FALL 2012
Toby Kenney
Homework Sheet 6
Model Solutions.
Basic Questions
1. The point (X, Y ) is uniformly distributed on the set
cfw_(x, y )|x + y < 3, y x > 1, x > 2
What is the conditional expectation of X given that Y = 2?
W
MATH/STAT 3360, Probability
FALL 2012
Toby Kenney
Homework Sheet 3
Model Solutions
Basic Questions
1. Three cards are drawn from a standard deck. Which of the following pairs
of events are independent?
There are exactly two queens
(a) The rst card is a he
MATH/STAT 3360, Probability
FALL 2014
Toby Kenney
Homework Sheet 8
Model Solutions
Basic Questions
Homework 7, Q.1 If X is exponentially distributed with parameter and Y is normally distributed with mean 0 and variance 2 ,
(b) Use the Cherno bound with t
MATH/STAT 3360, Probability
FALL 2014
Toby Kenney
Homework Sheet 3
Model Solutions
Basic Questions
1. Three cards are drawn at random (without replacement) from a standard
deck. Which of the following pairs of events are independent?
There is exactly one
MATH/STAT 3360, Probability
FALL 2014
Toby Kenney
Homework Sheet 5
Model Solutions
Basic Questions
1. If X is uniformly distributed on [0, 2], what is the probability density function of X 3 ?
1
1
We have P (X 3 < x) = P (X < x 3 ) = x23 , for 0 x 8, so t
MATH/STAT 3360, Probability
FALL 2014
Toby Kenney
Homework Sheet 6
Model Solutions
Basic Questions
1. X is normally distributed with mean 3 and standard deviation 2. Y is
independent and normally distributed with mean 5 and standard deviation
3. What is P
MATH/STAT 3360, Probability
FALL 2014
Toby Kenney
Homework Sheet 4
Model Solutions
Basic Questions
1. A random variable X has the following probability mass function:
x
0
2
3
4
9
25
P (X = x)
0.5
0.2
0.1
0.1
0.05
0.05
(a) What is E(X)?
E(X) = 0 0.5 + 2 0.
MATH/STAT 3360, Probability
FALL 2012
Toby Kenney
Homework Sheet 1
Due: Thursday 20th September: 2:30 PM
Basic Questions
1. A multiple choice exam has 15 questions, each of which can be answered
A, B, C, or D. In how many dierent ways could a student answ
MATH/STAT 3360, Probability
FALL 2012
Toby Kenney
Homework Sheet 5
Model Solutions
Basic Questions
1. If X is exponentially distributed with parameter 4, calculate the probability
density function of X 2 + 2X .
We know that P (X < x) = 1 e4x for any x
0.
MATH/STAT 3360, Probability
FALL 2011
Toby Kenney
Sample Midterm Examination
This Sample Midterm has more questions than the actual midterm, in order
to cover a wider range of questions.
1. How many ways are there to choose 5 students from a class of 25?
MATH/STAT 3360, Probability
FALL 2012
Toby Kenney
Homework Sheet 8
Model Solutions
Basic Questions
1. If X is exponentially distributed with parameter 1 and Y is exponentially
distributed with parameter 2 , where 2 > 1 :
(a) nd the moment generating funct
MATH/STAT 3360, Probability
FALL 2011
Toby Kenney
Midterm Examination
Model Solutions
Basic Questions
1. How many distinct ways can the letters of the word STATISTICS be
arranged.
There are a total of 10 letters, 3 S, 3 T, 2 I, 1 A and 1 C, so they
10!
ca
MATH/STAT 3360, Probability
FALL 2011
Toby Kenney
Sample Midterm Examination
Model Solutions
This Sample Midterm has more questions than the actual midterm, in order
to cover a wider range of questions.
1. How many ways are there to choose 5 students from
MATH/STAT 3360, Probability
FALL 2012
Toby Kenney
Homework Sheet 4
Model solutions
Basic Questions
1. What is the cumulative distribution function for the number of 6s rolled
on 5 fair (6-sided) dice?
The cumulative distribution function is given in the f