Question

3. (a) Let ? be a random variable with mean 3 and standard deviation 2, and let ? be a random variable with mean 4 and standard deviation 1. ? and ? have a correlation coefficient of – 0.3. Let = ? + ? .

Calculate:

(i) ???(? , ?)

(ii) ???(?) .

(b) ? has a Poisson distribution with mean 5 and ? has a Poisson distribution with mean 10. If ???(? , ?) = −12 , calculate the variance of ? where ? = ? − 2? + 3.

Answer 1