Depending on the input a computer program takes variable number of cycles to come up with the answer. Let X be the random variable which takes on the values k = 1,2,3,··· ,infinity for the number of cycles required to come up with the answer where 1 is the possibility that the program never arrives at an answer. (a) The probability mass function (p.m.f) for completing in k cycles is p_X(k) = (2^k)/(3^(k+1)) , k = 1,2,3,··· . What is the probability that the computer program never completes? (b) Use part (a) to find probability P (X greater or equal 3). Write your answer in a simplest fraction. (c) Given that the program has not found the answer after 2 cycles, what is the probability that it will never find the answer?

Name: Depending on the input a computer program takes variable number of cyc
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: Depending on the input a computer program takes variable number of cycles to come up with the answer. Let X be the random variable which takes on the values k = 1,2,3,··· ,infinity for the number of cycles required to come up with the answer where 1

Question

Depending on the input a computer program takes variable number of cycles to come up with the answer. Let X be the random variable which takes on the values k = 1,2,3,··· ,infinity for the number of cycles required to come up with the answer where 1 is the possibility that the program never arrives at an answer.

(a) The probability mass function (p.m.f) for completing in k cycles is p_X(k) = (2^k)/(3^(k+1)) , k = 1,2,3,··· .

What is the probability that the computer program never completes?

(b) Use part (a) to find probability P (X greater or equal 3). Write your answer in a simplest fraction.

(c) Given that the program has not found the answer after 2 cycles, what is the probability that it will never find the answer?