Many people fail to back up their computer systems regularly in spite of the pos

Question

Many people fail to back up their computer systems regularly in spite of

the possibility of catastrophic failure. The table below shows the joint

distribution of two Bernoulli random variables which indicate whether

the computer has a catastrophic failure (X) and whether the computer has

been backed up (Y).

a) What is the mean of X, E(X)? Give answer to two decimal places, without a leading zero.

b) What is the variance of X, V(X)? Give answer to two decimal places, without a leading zero.

c) What is the mean of Y? Give answer to two decimal places, without a leading zero.

d) What is the variance of Y? Give answer to four decimal places, without a leading zero.

e) What is the covariance between X and Y, Cov(X,Y)? Give answer to three decimal places, without a leading zero.

f) What is the correlation between X and Y, Corr(X, Y)? Give answer to two decimal places, without a leading zero.

Computer Failure Yes (X=1) No (X=0) Total Backup Yes (Y=1) .02 .13 .15 No (Y=0) .08 .77 .85 Total .10 .90

Explanation / Answer

a)Mean X =0.1

b)Var x=0.1-0.01 = 0.09

c)Mean Y = 0.02

d)Var Y = 0.02-0.0004 = 0.0196

e) Cov (XY) = E(XY) = 0.02

Computer Failure Yes (X=1) No (X=0) Total yp y^2p xy*P(XY) Backup Yes (Y=1) 0.02 0.13 0.15 0.02 0.02 0.02 No (Y=0) 0.08 0.77 0.85 0 0 0 Total 0.1 0.9 0.02 0.02 0.02 xp 0.1 0 0.1 x^2p 0.1 0 0.1

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