Consider an experiment in which a fair four-sided die (with faces labeled 0, 1, 2, 3) is thrown once to determine how many times a fair coin is to be flipped. in the sample space of this experiment, random variables n and k are defined by • n = the result of the die roll • k = the total number of heads resulting from the coin flips determine and sketch each of the following functions for all values of their arguments:
(a) pn (n)
(b) pk|n (k | 2)
(c) pn|k(n | 2)
(d) pk(k)
(e) also determine the conditional pmf for random variable n, given that the experimental value of k is an odd number.
(f) finally, compute the expected value and variance for each of the distributions found in parts (a)–(e).