1. At Shoe World, the manager nds the probability that a woman will buy 1, 2, 3, or 4 pairs of shoes as given in Table 1. (a) Find the mean, variance and standard deviation for the distribution of the number of shoes. (b) Comment on whether the distribution is positively or negatively skewed. (c) During festive seasons, the manager nds that the purchases usually double. Let Y be the number of shoes that a woman will buy during festive period. i. Give the probability distribution of Y ii. Find the mean and variance for this probability distribution. iii. Find P(X + 1