Assume that the numbers of car accidents happened in a year X follow a Poisson distribution Poisson (X) with probability mass function as: Xx f(x|X) exp(-X). x! From previous studies we know that the prior distribution of the parameter λ is given as follows 1 π(λ)α 1 + X ² * Please answer the following questions: (a) Write down the posterior distribution for X, up to a normalising constant. [2 marks] (b) Write down the R command to simulate a random value lambda from a Gamma distribution with shape parameter a and rate parameter b. [2 mark] (c) Write down the R command to simulate a random value U from a standard Uniform distribution. [2 mark] (d) Write down a rejection sampling method to simulate from the posterior distribution of X, provided that you can simulate random values from a Gamma distribution. Note you don't need to write R code for question (d).