Question: 1. Two cards are picked in succession (without replacement) from a standard deck. If o is an outcome, let X(o) equal the sum of the numbers on the cards if both cards are numbered; X(o) = 11 if exactly one card is a jack, queen, king or ace; and X(o) = 12 if two of the cards are in the jack, queen, king, ace group. Determine the probability distribution for X, as well as its mean and standard deviation.
2. An experiment is to choose any integer from 1 to 30, inclusively. If o is an outcome, let X(o) = 1 if o is divisible by 2, X(o) = 2 if o is divisible by 3 but not 2, and X(o) = π otherwise. Determine the probability distribution of X, and its mean and standard deviation.