My last question I mixed the data and the question, my bad! 5) Given below is a bivariate distribution for the random variables x and y . f(x, y) x y 0.2 50 80 0.5 30 50 0.3 40 60 Compute the expected...

My last question I mixed the data and the question, my bad!

5)
Given below is a bivariate distribution for the random variables
x
and
y.

1. Compute the expected value and the variance for
   x
   and
   y.


2. Develop a probability distribution for
   x
   +
   y.


3. Using the result of part (b), compute
   E(x
   +
   y) and
   Var(x
   +
   y).


4. Compute the covariance and correlation for
   x
   and
   y. Are
   x
   and
   y
   positively related, negatively related, or unrelated?


5. Is the variance of the sum of
   x
   and
   y
   bigger, smaller, or the same as the sum of the individual variances? Why?