ORIE 360/560 Fall 2007
Assignment 6
Due Tuesday, Oct. 16 at 2:00 pm
Please remember to show your work!
Please remember to put your section number and net id on the
assignment!
Problem 1.
Suppose
X
has an exponential distribution, and that
P
[
X > .
01] = 1
/
2.
Find the unique
number
t
satisfying
P
[
X > t
] =
.
9.
Problem 2.
If
X
has density
f
X
(
x
) =
1
2
λe

λ

x

, for
x
∈
R
, then
X
is said to have the
double exponential
distribution with parameter
λ
. Find the mean and variance of such a random variable.
Hint: you could use
moment generating functions, although it’s not required.
Problem 3.
Find the moment generating function of the binomial(
n, p
) random variable, where
n
≥
1 and
0
< p <
1. Use the result to check the values for the mean and variance given in class (or in the text).
Problem 4.
A contractor purchases a shipment of 100 widgets, 20 of which are defective.
(a) If the contractor tests the widgets one by one, what is the probability that the first defective widget will
be discovered on the 15th trial?
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 Fall '07
 EHRLICHMAN
 Probability theory, 25%, 75%, cdf FX

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