Contention Resolution Instructor : Thomas Kesselheim 1 Waiting for One Success

Assume you are rolling a dice over and over again. How long to expect until it shows “6” for the first time? More generally, we observe a random process that is either “successful” or “not successful” in every round. All rounds are independent and in each we get the outcome “successful” with probability p. Let T denote the random variable indicating the number of rounds it takes until we see “successful” for the first time. As it is a non-negative integer random variable, we can use the following formula to calculate the expectation. E [T ] = ∞ ∑