a$)$ Using loop in $R$ to evaluate $($approximate$)$ the expectation of binomial distributed random variables having the following probability mass function.

$P(x=k)=([n],[k])p^k(1-p{)}^{n-k}$ for $k=0,1,2,$cdotsn

Compute the expectation using the definition of the expectation of a discrete random variable, not a short cut formula for a binomial random variable. In your approximation, consider $n=10,20$ and $30$ with $p=0\mathrm{.}25$ and $0\mathrm{.}6$ respectively. Your code should loop through the values of $n$ and $p,$ and for each combination of $n$ and $p,$ it should loop through each value of $x$ in the definition of the expected value. Store your values in a matrix called expected. Do NOT use the built$-$in function dbinom$()$ for this question.

b$)$ Based on the $R$ code in part $($a$),$ create an $R$ function called BinExp that can return the approximated expectation of a binomial distributed random variable with any given $n>1$ and pin$(0,1).$