R code that gives results like Wolfram Alpha for the expectation of a function of a random variable? When I ask Wolfram Alpha to calculate $E[f(X)]$ where $f(x) = e^{-x^2}$ and $X \sim \mathcal{N}(1,4)$, it gives the result
$$
E[f(X)] = \frac{1}{3\sqrt[9]{e}} \approx 0.29828,
$$
and the following plot which appears to be based on taking a number of simulations:

How can I generate the same type of plot using R?
You can simulate one of these lines like this:
library(ggplot2)
X&lt;-rnorm(1000, 1, sqrt(4))
f&lt;-function(x) exp(-x*x)
df&lt;-data.frame(sample_size=seq_len(1000), sample_means=cumsum(f(X))/seq_len(1000))
ggplot(df, aes(x=sample_size, y=sample_means)) + 
geom_line() + theme_minimal() + labs(x=NULL, y=NULL)