For sample size $M=100,500,1000,2000,$ compare the mean and standard devi$-$

ations of the estimates. $($in r programming language$)$

$($c$)($For graduate students $862$ only$)$ Implement MC integration using self$-$normalized

importance sampling with $g(x)$ from a mixture normal density. Explain the pro$-$

cedure and integrate your results clearly.