Statistics Solutions

(Step-by-Step) Lifelenghs of memory chips. The lifelength Y (in years) of a memory chip in a laptop computer is a Weibull random variable with probability

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

\[f(y)=\left\{ \begin{matrix} \frac{1}{8}y{{e}^{-{{y}^{2}}/16}} \\ 0 \\ \end{matrix}\text{ }\begin{matrix} \text{if }0\le y<\infty \\ elsewhere \\ \end{matrix} \right.\]
  1. What are the values of \[\alpha \text{ and }\beta ?\]
  2. Compute the mean and variance of Y.
  3. Find the probability that a new memory chip will not fail before 6 years.

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