In a model of hardware failure per week for the JJ Computer Lab we get the follo
ID: 3130193 • Letter: I
Question
In a model of hardware failure per week for the JJ Computer Lab we get the following:
Probability of no failures = .16
Probability of 1 failure = .28
Probability of 2 failures = .24
Probability of 3 failures = .18
Probability of 4 failures = .08
Probability of 5 failures = .04
Probability of 6 failures = .02
Suppose X = the number of failures in the JJ Computer Lab during 1 week.
a. What is the probability that X>=3?
b. Calculate the expected value of X?
c. Calculate the variance of X.
d. Calculate the standard deviation of X.
e If the manager loses L=X2+3 dollars what is the expected value of L?
f. Write an R Script simulating 50 independent observations of X.
Explanation / Answer
a.The probability that P(X>=3)=P(X=3)+P(X=4)+…+P(X=6)
=0.18+0.08+0.04+0.02=0.32
b.The expected value of X is:
0*0.16+1*0.28+…+6*0.02
=1.94
c.The variance is: (0-1.94)^2*0.16+…+(6-1.94)^2*0.02
=2.0964
d.The standard deviation is sq rt of 2.0964=1.45
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