Answer:
Step-by-step explanation:
For this case we have the following distributions given:
The expected value for x is
And the variance
The expected value for x is
And the variance
We define a new random variable:
We need to find the expectd value and the variance for W.
For the expected value we have this:
And if we replace the parameters we got:
Now foe tha variance of W we know that X and Y are indpenendet variable so then
For this case we can use the property that is a is a constant and X a random variable then , and we got this:
And if we replace we got: