Problem 2: Let us consider the binomial distribution of a random variable X with parameter n=20 and following probabilities p. Probability (p) 0.01 0.05 0.20 0.35 0.50 0.65 0.80 0.95 0.99 E Determine the mean, standard deviation, skewness and kurtosis in each case of X. (ii) When the standard deviation is smallest? (iii) Sketch the graph of the variance of X as a function of p. (iv) Using calculus or otherwise show that the variance is largest when p=0.50