A number n is chosen at random from the set 12 20 We are int

A number n is chosen at random from the set {1,2,..., 20}. We are interested in k, the integer power of 2 which exactly divides n. Recall that we say that 2^k exactly divides n if 2^k|n but 2^k + 1|n. We write \"a || b\" for \"a exactly divides b\" Set up a probability space to model this experiment. Define k formally as a random variable. (What kind of thing is a random variable?) Find the support of k. Find the range of k. Find the events \"k = i\" explicitly for every i in the range of k. Find the probability function of k. Is k a Bernoulli random variable? A Binomial r. v.? A discrete r. v.?

Solution

n={1,2,3,....20} random variable chosen from this space.

(a).     f(k) = a if 0< k< 4

                 = b if k > 5

(b) here k is not a random variable, because random variable is the numericl quantities which can\'t be predicted. here k is the integer values and starting from the 0, 1, 2, 3,.......

(d) k >= 0