Electronic components of a certain type have a length of life $X$, measured in hours with probability density given by

$$f(x) = \begin{cases} \frac{1}{150}e^{-\frac{x}{150}} & x > 0 \\ 0 & \mbox{ otherwise } \\ \end{cases}$$

Suppose that three such components operate independently and in parallel in a certain system as shown in the diagram below. Which statement best describes the distribution of $Y$, the length of life of the entire system?

Which statement best describes the distribution of $Y$, the length of life of the entire system?

A. $Y = max(X_1, X_2, X_3)$, $Y\,$ is not an exponential random variable.
B. $Y = min(X_1, X_2, X_3), Y\,$ has an exponential distribution with a mean of 50.
C. $Y = max(X_1, X_2, X_3), Y\,$ has an exponential distribution with mean of 450.
D. $Y = min(X_1, X_2, X_3), Y\,$ has an exponential distribution with a mean of 450.
E. $Y = max(X_1, X_2, X_3), Y\,$ has an exponential distribution with a mean of 50.