An information source generates symbols at random from a four-letter alphabet {a, b, c, d} with probabilities

P r[a] = 1/2,
P r[b] = 1/4,
P r[c] = 1/8,
P r[d] = 1/8.

A coding scheme encodes these symbols into binary codes as follows:

0
10
110
111

Let X be the random variable denoting the length of the code, ie, the number of binary symbols

a. What is the range of X?
b. Sketch the cdfF_X (x) of X and specify the type of X
c. Find P(X≤1),P(X>1)& P(1≤X≤2)