PES 2. The length of time to failure (in hundreds of hours) for a transistor is a random variable Y with distribu- tion function given by F() = er, y20. Find the .81-quantile, 4.81 of Y. Round answer to 6 decimal places. (4PLS ) 3. 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 f ( ) = 127, 0 Sys1, 10, elsewhere. (a) (2 pts) Find E(Y) and V(Y). Answers can be left as fractions. (b) (2 pts) For a robot under study, the profit X for a week is given by X = 300Y - 40. Find E(X) and V(X)