solve the following questions 1) Let X be a binomially distributed variable with parameters n and p. Show that (P(X=k))/(P(X=k+1))=(k+1)/(n-k)*(1-p)/p, where k = 0, 1, ... , n-1. 2)Find the mean and the variance of the uniform probability distribution given by f(x) = 1/n for x = 1, 2, 3, ... , n. Hint: The sum of the first n positive integers is n(n+1)/2 and the sum of their squares is n(n+1)(2n+1)/6. 3) Find the upper limit provided by Chebyshev's theorem and also the exact probability that a binomially distributed random variable with n=16 and p=1/2 will obtain a value differing from the mean by at least 3 standard deviations.