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

It is not standard question. It is needed to clarify it. – Hamed Baziyad Apr 19 '20 at 13:33 — Hamed Baziyad, Apr 19 '20 at 13:33

score 2 · Answer 1 · answered Apr 19 '20 at 12:37

I will not solve for you the exercice but give you the clue on how to solve it

You need to do as the exercice does:

Simulate U[0,1]
Simulate N(0,1)

Put them together using a value for p

For a given p, you can define a function:

set.seed(234)
computeX <- function(p){

  u <- runif(1000)
  z <- rnorm(1000)

  X = p*z + (1-p)*u
  return(X)
}

var(computeX(0.2))
[1] 0.08924463

Now I let you find the routine to get p that is needed for your exercice.

No need for any external library

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 — Andrea Garcia, Apr 19 '20 at 17:47

score 1 · Accepted Answer · answered Apr 19 '20 at 22:01

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

R Proble with Monte Carlo Simulation

2 Answers2