IE 575 Fall 2013 Homework 3
Due on Tuesday, October 22
nd
1. Let X be a random variable with PDF
2
() = cfw_ 3 1 < < 2
0
And let Y = 2 .
Calculate E[Y] and var[Y].
2. You are allowed to take a certain test three times, and your final score will be the m
IE 575 Fall 2013 Homework 4
1.
The transform associated with a random variable Y has the form
() = 6 (0.1 + 2 + 0.1 4 + 0.4 7 )6
Find a, (41), (11), the third largest possible value of Y, and its corresponding probability.
2.
The transform and the mean a
IE 575 Fall 2013 Homework 3 Solution
Due on Tuesday, October 22
nd
1. Let X be a random variable with PDF
2
() = cfw_ 3 1 < < 2
0
And let Y = 2 .
Calculate E[Y] and var[Y].
2. You are allowed to take a certain test three times, and your final score will
IE 575 Homework 2 Solution
1.
The annual premium of a special kind of insurance starts at $1000 and is reduced by 10% after each year where no
claim has been filed. The probability that a claim is filed in a given year is 0.05, independently of preceding
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but he leaves a sample (one can) only on those calls for which the door is answered
and a dog is in residence. On any call the probability of the door being answared is
IE 575 Homework 2 Due Sep 27,Friday
1.
The annual premium of a special kind of insurance starts at $1000 and is reduced by 10% after each year where no
claim has been filed. The probability that a claim is filed in a given year is 0.05, independently of p
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IE 575 Fall 2013
Tutorial 1
September 12, 2013
1. Let A and B be events such that A B. Can A and B be independent?
Answer:
If A B, then P(B A)= P(A) But we know that in order for A and B to be independent, P(BA)=
P(A)P(B). Therefore, A and B are independe
IE 575 HW1
Due Friday, Sep 20th
1. Fully explain your answers to the following questions:
a. If events A and B are mutually exclusive and collectively exhaustive, are
B c mutually exclusive?
b. If events A and B are mutually exclusive but not collectively
[E 575 Solutions to Practlce Questions for Exam ll
Solution to Problem 3.1. The random variable Y = 9(X) is discrete and its PMF
is given by
Wu) = P0: 51/3): 1/3! py(2)=1 -Pr(1)= 2/3-
Thus,
1 2 5
1_._. _. _
Em 31+3 2 3
The same result; is obtained using t
IE575 Fall 2013
Tutorial 3
09/24
IE575 Fall 2013
Tutorial 3
09/24
*Todays tutorial is a bit challenging and you are not expected to do them all.
Problem 1. For each one of the statements below, give either a proof or a
counterexample showing that the stat
IE575 Fall 2013
Tutorial 8
11/14
1.
IE575 Fall 2013
Tutorial 8
11/14
IE575 Fall 2013
Tutorial 8
11/14
2. Type A, B, and C items are placed in a common buffer, each type arriving as part of an
independent Poisson process with average arrival rates, respect
IE575 Fall 2013
Tutorial 8
11/14
1.
IE575 Fall 2013
Tutorial 8
11/14
2.Type A, B, and C items are placed in a common buffer, each type arriving as part of an
independent Poisson process with average arrival rates, respectively, of a, b, and c items
per mi
IE575 Fall 2013
Tutorial 7
10/31
1. X and Y are independent and have PDFs as shown below. Let W = X+Y and find
using a graphical argument.
IE575 Fall 2013
Tutorial 7
10/31
IE575 Fall 2013
Tutorial 7
10/31
2. Let X=Y-Z where Y and Z are nonnegative random
IE575 Fall 2013
Tutorial 7
10/31
1. X and Y are independent and have PDFs as shown below. Let W = X+Y and find
using a graphical argument.
2. Let X=Y-Z where Y and Z are nonnegative random variables such that YZ=0.
(a) Show that cov(Y,Z)<=0;
(b) Show that