#------------------------------
#
# GdA May 2020
#----------------------------------

ft <- function(t,r) r^2*t*exp(-r*t)

r = 1
t <- seq(0, 8, len=101)
plot(t, ft(t,r), ty='l', col='blue', lwd=1.8, ylim=c(0,1), ylab="f(t)")
points(t, r*exp(-r*t),  ty='l', col='red', lty=2, lwd=1.8)
abline(h=0)
abline(v=0)

E.t <- integrate(function(t) t*ft(t,r), 0, 10)$value
cat(sprintf("E(t) = %.4f\n", E.t))
E.t2 <- integrate(function(t) t^2*ft(t,r), 0, 10)$value
cat(sprintf("sigma(t) = %.4f\n", sqrt(E.t2-E.t^2)))