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