Consider a process in which there is one trial per click (a click is a unit of t

Question

Consider a process in which there is one trial per click (a click is a unit of time), starting with click number 1. Each trial results in success with probability p, or in failure with probability 1 - p. Define the following random variables: Xm is the number of successes achieved in the first, m clicks, i.e., during the time interval t Xn is the number of successes achieved in the first n clicks, i.e., during the time interval where n > m in all parts of this problem. Tj is the time (click index) at which the jth success occurs. Tk is the time (click index) at which the Kth success occurs, where k > j in all parts of this problem. In terms of the variables Xn and Tk find the following pmfs and conditional pmfs: pXn(k) is the probability that there are k successes in the first n clicks. Write a formula for pXn(k). pXn|Xm(k|i) is the probability that there are k successes in the first n clicks, given that there are i successes in the first m clicks, where m

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300 points is not fair :(

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