Suppose we have N independent samples of some random variable. The samples are used to create a histogram based on just two bins. Suppose the probability that a sample is in binl is p1 and the probability that the sample is in bin2 is p2. Let X1 be the number of samples that are in bin'l, and X2 be the number of samples that are in bin2. The fit test {'2 in this case is described by: (a) Show that the random variable X1 follows a binomial distribution X1~B(N,p'l). What is the distribution of the random variable X2? Are X1 and X2 independent? What is the mean and variance of X1. Hint: You can use known results for the mean and variance of a random variable with a binomial distribution. (b) Show now that the test of fits {'2 can be fully expressed in terms of X1 and p'l