R Proble with Monte Carlo Simulation

Question

How I could solve this exercise:

Let U come from a uniform (0,1) distribution and Z come from a standard normal distribution. Let X = pZ + (1-p)U. Estimate p when X has a variance of 0.4.

Maybe I should install.packages('polynom')?

p is equal to 0,62 because I´ve already calculated it analitically, but I don´t know how to solve it with R using random random numbers generators

Answer 1

Here is an example

fobj <- function(p)  abs(var(p*rnorm(1e5) + (1-p)*runif(1e5))-0.4)
pval <- optimise(fobj,c(0,1))$minimum

where

• first define your objective function fobj, i.e., distance between variance of X and 0.4
• then apply optimise minimize the fobj

Result

> pval
[1] 0.6223968