Solve this problem using R$.$ Please include the R code for practice.

The kth moment about zero is defined by $E((x-{}_x{)}^k),$ the kth standardized moment is defined by $E[(\frac{x-{}_x}{{}_x}{)}^k]$ when $k=4$ we call the last term

the kurtosis $($bulging$).$

Calculation

Use the following table to calculate the kurtosis:

Values of $x$ and $P(x)$

Make an $R$ function to carry out the calculation it must print a named list containing the mean, variance, and kurtosis.