STAT 400 Fall 2011 Version A
Name Quiz 2
(10 points)
ANSWERS
.
Be sure to show all your work; your partial credit might depend on it.
No credit will be given without supporting work.
1. (10) Initech does part of its business via Internet. However, because of the high traffic, the
server that carries the company's website often crashes. The probability distribution of the number of server crashes per week, X, is given below:
x
0 1 2 3
f (x) 0.55 0.25 0.15 0.05
x f (x) 0 0.25 0.30 0.15
x 2 f (x) 0 0.25 0.60 0.45
0.70
1.30
If the server does not crash, Initech's weekly profit from the website is $50,000. However, each time the server crashes, Initech looses $20,000. Therefore, Initech's weekly profit from the website (in thousands of $) is Y = 50 20 X. Find Initech's average weekly profit from the website and its standard deviation.
E( X ) =
x f ( x)
all x
= 0.70.
Var ( X ) = E ( X 2 ) - [ E ( X ) ]
2
=
x 2 f ( x) - [ E ( X ) ] 2
all x
= 1.30 - ( 0.70 )
2
= 0.81.
SD ( X ) =
0.81 = 0.90.
E ( Y ) = 50 20 E ( X ) = 50 20 0.70 = 36. SD ( Y ) = | 20 | SD ( X ) = 20 0.90 = 18.
$36,000. $18,000.
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