Question

Refer to exercise 12. let z = x + y represent the total number of repairs needed.

a. find μz .
b. find σz .
c. find p(z = 2). statistics for engineers

Answer 1

Assuming the question I linked is the same as yours, you should have the following information (provided you completed exercise 12):


`\mu_X=1.01`

`\mu_Y=1.23`

`\sigma_X\approx0.89994`

`\sigma_Y\approx0.99855`

`\mathrm{Cov}(X,Y)\approx0.2377`

`\rho_(X,Y)\approx0.264512`

Given that
`Z=X+Y`, we have


`\mu_Z=\mu_X+\mu_Y=2.24`


`\sigma_Z=\sigma_X+\sigma_Y+2\,\mathrm{Cov}(X,Y)\approx1.51076`

Finally,
`Z=2` is the same as the event that any one of the following occurs:
`X=0` and
`Y=2`;
`X=1` and
`Y=1`; or
`X=2` and
`Y=0`. So we have


`\mathbb P(Z=2)=0.02+0.16+0.07=0.25`