Homework SourseMany people fail to back up their computer systems regularly
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 two decimal places, without a leading zero.
e) What is the covariance between X and Y, Cov(X,Y)? Give answer to two 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 | .28 | .30 |
| No (Y=0) | .08 | .62 | .70 | |
| Total | .10 | .90 |
Solution
a)E(x)=1*0.1+0*0.9=0.1
b)V(x)=E(x2) - E(x)2 =0.1-0.1=0
c)E(y)=0.3
d)V(y)=0
e)cov(x,y)=0.03
