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?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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
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?
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