Assume that an n-bit integer (represented by standard binary notation) takes any value in the range 0 to 2^n − 1 with equal probability.

(a) For each bit position, what is the probability of its value being 1 and what is the probability of its value being 0?

(b) What is the average number of “1” bits for an n-bit random number?

(c) What is the expected value for the position of the leftmost “1” bit? In other words, how many positions on average must we examine when moving from left to right before encountering a “1” bit? Show the appropriate summation.