Choose ONE of the random variables from the options provided ineach part. (a) Confirm the essential properties of the probabilityfunction for the binomial or Poisson or geometric random variable.[5 marks] (b) Derive the mean of the binomial or Poisson orgeometric random variable from first principles (i.e. using theprobability function and the definition of expectation). [7 marks](c) Confirm the essential properties of the probability densityfunction for the uniform or exponential random variable. [5 marks](d) Derive the cumulative distribution function for the uniform orexponential random variable. Show that this function meets thenecessary requirements for such a function (state what these are,and show that they are met). [8 marks] (e) Derive P(x1 < X
