If a fair die is thrown, then each number from 1 to 6 has the same chance of being the outcome. Let \(X\) be the random variable to indicate whether the outcome is 5, i.e.,

\[X=\left\{\begin{array}{l}1 \text { if the outcome is } 5, \\0 \text { if the outcome is not } 5 .\end{array}\right.\]

(a) Describe the distribution of \(X\) and find the mean and variance of \(X\).

(b) For a sequence of i.i.d. variables that follow the distribution, find the limit of the sample mean.