In Exercise 84, set n = ∞ and find the expected value of the number of the first success.

Exercise 84

Suppose that in a sequence of n independent trials, the common probability of success is a random variable; say, it depends on conditions under which the trials are being performed.
(For example, in the quality control scheme, the share of defected items may depend on conditions under which the particular batch of items had been manufactured, and may vary from day to day. However, we assume that, given the probability of success (for example, we know it for a particular batch), the trials are independent.) In the general scheme, denote by Θ the (random) probability of success. Find the expected value of the number of successes in the following situations.