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g <- function(x) { 3 * x^2 / 8 } # define pdf
integrate(f,lower=0,upper=2) # check it is a pdf
xg <- function(x) { x * g(x) }
integrate(xg,lower=0,upper=2) # expected value
xxg <- function(x) { x^2 * g(x) }
integrate(xxg,lower=0,upper=2) # E(X^2)
# compute the variance using E(X^2) - E(X)^2
integrate(xxg,lower=0,upper=2)$value -
(integrate(xg,lower=0,upper=2)$value)^2
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