Question

The proportion of time Y that an industrial robot is in operation during a 40-hour week is a random variable with probabilitydensityfunction

f ( y ) =[ 2 y , 0 ��������� y ��������� 1,
0 , elsewhere.
E(Y)=2/3
E(Y^2)=1/2
V(Y) = 1/ 18
Question: For the robot under study,the profit represented as X for a week is given by
X = 200Y -60. Find E(X) and V(X)?

Answer 1

f(y) = 2y when between 0 and 1
0 else where

Answer 2

profit equation is X=200Y -60
How do I find V(X)?