$($a$)$ Write a R function whose inputs are $n$ and a vector $p=|p_1,p_2,$dots,$p_n|,$ such that it outputs instance, $p=[\frac{1}{6},\frac{1}{6},\frac{1}{6},\frac{1}{6},\frac{1}{6},\frac{1}{6}]$ corresponds to a fait sit$-$sided dice.

$($b$)$ Suppose you start with $0$ dollars and decide to play s ganditing game. Yow pwey $3\mathrm{.}5$ dollars, roll a firir dice, and win $k$ dollars if a $k$ is rolled. Yoe ply this game $20$ times. Let $S_1$ be $3000$ times, plot your resulis as a histogrsm, sad report the ompirical ment and empirical varianse of $S_1.$

$($c$)$ Suppose you start with $0$ dollars and decide to play a gambiting game. You poy $3\mathrm{.}5$ dollars, roll a bissed dice such that the probablity of rolling a $1$ and $6$ are each $\frac{1}{4},$ and win $k$ dollars ufturwards $($which can be negative$).$ Run this sitmelation $100$ timess plet jour resulks as a histogram, und report your empirical mest and empitical sariatere of $S_2.$

$($d$)$ Comysure your results for $S_1$ and $S_2.$ Do they mokle intuitine sensel$?$