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1. Two close friends live in different states. The probability mass function for the number or meetings of two friends in a one-year period is given by random variable X is as follows: x = 1, 2,3,4 P(X =x)={3) else Rewrite this pmf in a table form. b. Determine the 'c' value so that the function given is a valid probability mass function. Justify your answer by showing that the pmf is valid. Derive the cumulative density function (cdf) - present it in functional form like this a. с. some#1 x< smthl some#2 smthl

1. Two close friends live in different states. The probability mass function for the number or meetings of two friends in a one-year period is given by random variable X is as follows: x = 1, 2,3,4 P(X =x)={3) else Rewrite this pmf in a table form. b. Determine the 'c' value so that the function given is a valid probability mass function. Justify your answer by showing that the pmf is valid. Derive the cumulative density function (cdf) - present it in functional form like this a. с. some#1 x< smthl some#2 smthl

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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1. Two close friends live in different states. The probability mass function for the number of in-person meetings of two friends in a one-year period is given by random variable X is as follows: x = 1,2,3,4 C P(X =x) =: else Rewrite this pmf in a table form. b. Determine the 'c' value so that the function given is a valid probability mass function. Justify your answer by showing that the pmf is valid. Derive the cumulative density function (cdf) - present it in functional form like this a. с. some#1 x< smthl some#2 smthl < x< smth2 P(X <x) =: x > smth.. d. Graph the cdf in some way (by hand, excel, desmos, etc.,). Label the x-axis as x and the y-axis as F(x). Make sure the values of x range from 0 to 5. What is the probability that two friends meet at most three times in a one-year period f. е. What is the probability that two friends meet at least two times in a one-year period g. What is the probability that two friends meet more than one time but less than four times in a one- year period h. What's the long run average number of meetings (expected value)? i. Graph the pmf using a column chart or by hand. Label the x-axis as c and the y-axis as f(c). Mark the expected value on this graph. j. Imagine each meeting costs $500 per person. What's the expected cost to the two friends based on meeting costs? k. What's the variance of the number of meetings? 1. What's the standard deviation of the number of meetings?
Transcribed Image Text:1. Two close friends live in different states. The probability mass function for the number of in-person meetings of two friends in a one-year period is given by random variable X is as follows: x = 1,2,3,4 C P(X =x) =: else Rewrite this pmf in a table form. b. Determine the 'c' value so that the function given is a valid probability mass function. Justify your answer by showing that the pmf is valid. Derive the cumulative density function (cdf) - present it in functional form like this a. с. some#1 x< smthl some#2 smthl < x< smth2 P(X <x) =: x > smth.. d. Graph the cdf in some way (by hand, excel, desmos, etc.,). Label the x-axis as x and the y-axis as F(x). Make sure the values of x range from 0 to 5. What is the probability that two friends meet at most three times in a one-year period f. е. What is the probability that two friends meet at least two times in a one-year period g. What is the probability that two friends meet more than one time but less than four times in a one- year period h. What's the long run average number of meetings (expected value)? i. Graph the pmf using a column chart or by hand. Label the x-axis as c and the y-axis as f(c). Mark the expected value on this graph. j. Imagine each meeting costs $500 per person. What's the expected cost to the two friends based on meeting costs? k. What's the variance of the number of meetings? 1. What's the standard deviation of the number of meetings?
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