Question: Lifelenghs of memory chips. The lifelength Y (in years) of a memory chip in a laptop computer is a Weibull random variable with probability density

\[f(y)=\left\{ \begin{matrix}

\frac{1}{8}y{{e}^{-{{y}^{2}}/16}} \\

0 \\

\end{matrix}\text{ }\begin{matrix}

\text{if }0\le y<\infty \\

elsewhere \\

\end{matrix} \right.\]

a. What are the values of \[\alpha \text{ and }\beta ?\]

b. Compute the mean and variance of Y.

c. Find the probability that a new memory chip will not fail before 6 years.