A public electricity supplier has a number of facilities numbered from 1 to 19. We suppose that for i = 1, 2,..., 19 , installation i produces (100*i) MW.

N: the number of installations that works among all 19 facilities

C: the total electricity production.

Calculate the mean and variance of C if:

a) all possible combinations of plants that work are equally probable ; b) all S_N elements are equally likely.

I think there is a total of 524 287 total combinations possible and they are equally probable. The thing is I don't really notice a difference between a) and b).

to calculate the number of combinations, I used this equation 19!/(2!x17!) for a combination of 2 facilities, and i repeated from a combination of 1 to 19 facilities that are functional

I think I will use those 2 equations

E[C|N] = SUM(x_i*p_C|N(x_i))

VAR[C|N] = E[C^2|N]-(E[C|N])^2