The following is a question possibly involving "Expected Values for Continuous Random Variables" and/or "The Uniform Probability Distribution".

Don't worry too much details in steps.

I will mark as helpful if correct. Thanks!

The proportion of time Y that an industrial robot is in operation during a 40-hour week is a random variable with probability density function _ 392, 0 S y S 1 fly) _ l 0, otherwise For the robot under study. the prot X for a week is. given by X = 200Y 60. Find the variance of prot for a week