I just need help with number 2 question Thank you in advance

I just need help with number 2 question. Thank you in advance!!!!

Solution

The expectation is given as:

E [x] = x p(x)

Thus here, we have,

E [R] = r p₁         and            E [D] = d p₂

Further, variance is given as:

V(X) = E [x²] - (E [x])²

Therefore,

V(R) = E [R²] - (E [R])²

where

E [R²] = r² p₁

That is,

V(R) = r² p_{1 -} (r p₁)²

or

V(R) = r² p₁ ( 1 - p₁)

Similarly,

V(D) = d² p₁ ( 1 - p₁)