How to integrate a function in R?

Question

In R, I am trying to integrate the following function and verify that it is a pdf, as well as get the expected value and variance.... though I'm not entirely sure how to do this.

The function that needs to be verified is: f(x) = (x/4)*e^((-x^2)/8), x >= 0.

So far, I only have:

fun = expression((x/4)*e^((-x^2)/8))
integrate(fun,0,Inf)

It states error with the code above...

I know to get the expected value would be:

mean(x)

and the variance would be:

vcov(x)

Answer 1

You need to pass a function into integrate

fun = function(x) {(x/4)*exp((-x^2)/8)}
integrate(fun,0,10)

# Mean
fun2 = function(x) {x*fun(x)}
integrate(fun2,0,Inf)

# Variance
fun3 = function(x){(x-2.506628)^2 * fun(x)}
integrate(fun3,0,Inf)