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ISyE 2027
Probability with Applications
Fall 2006
R. D. Foley
Homework 5
October 4, 2006
due on Tuesday
1. Suppose you are selling bagels. What would be a reasonable guess as to the distribution of (a) the
number of customers that enter the store during the next hour? (b) the number of customers that pay
for their bagels until a customer drops their change? (c) the number of customers out of the next ten
that pay with a twenty dollar bill?, and (d) whether all of the bagels are sold or not?
2. Suppose
X
is a random variable with probability mass function Pr
{
X
=
k
}
=
ck
for
k
= 1
,
2
,
3
,
4, and
Y
= (
X

2)
2
. (a) Determine
c
. (b) Compute E[
X
]. (c) Compute the probability mass function of
Y
.
(d) Compute E[
Y
]. (e) Compute the conditional probability mass function Pr
{
X
=
k

X
≤
2
}
.
3. Suppose
Y
is a Bernoulli random variable with parameter
p
= 1
/
3. (a) Compute E[
Y
]. (b) Let
Z
= (
Y

1
/
3)
2
. Find the probability mass function of
Z
. (c) Compute E[
Z
].
4. Suppose
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This note was uploaded on 02/01/2010 for the course ISYE 2027 taught by Professor Zahrn during the Spring '08 term at Georgia Institute of Technology.
 Spring '08
 Zahrn

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