Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2012 / Paper 1 / 18 / c / i / Solution

Normalize the probability density function on its nonnegative support:The integral follows from one integration by parts, with the boundary term zero since $\lambda >0$. Hence $A={\lambda }^2$. This is a gamma distribution of shape $2$ and rate $\lambda$.