1. Random Variables An information source generates symbols at random from a four-letter alphabet {a, b, c, d} with probabilities P(a) = 1, P(b) = 1, and P(c) = P(d) = 1. A cod- ing scheme encodes these symbols into binary codes as follows: a O b 10 C 110 111 Let X be the r.v. denoting the length of the code-that is, the number of binary sym- bols (bits). (a) What is the range of X? (b) Assuming that the generations of symbols are independent, find the probabilities P(X = 1), P(X = 2), P(X = 3), and P(X > 3)