Given twelve civilians who are wearing socks and each one of them have various (unique) styles. An authority asked all the civilians to place their socks all in one container, jumbling them all, and he randomly selected 6 pieces of socks. Given a random variable X, which is the amount of matching sets or pairs of socks, find the probability mass function of variable X. Also give the moment-generating function of X and utilize it to find the mean and variance of X

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...
icon
Related questions
Question

Hint: It is about Poisson Distribution of discrete probability

Given twelve civilians who are wearing socks and each one of them have various (unique) styles. An
authority asked all the civilians to place their socks all in one container, jumbling them all, and he
randomly selected 6 pieces of socks. Given a random variable X, which is the amount of matching sets or
pairs of socks , find the probability mass function of variable X. Also give the moment-generating
function of X and utilize it to find the mean and variance of X
Transcribed Image Text:Given twelve civilians who are wearing socks and each one of them have various (unique) styles. An authority asked all the civilians to place their socks all in one container, jumbling them all, and he randomly selected 6 pieces of socks. Given a random variable X, which is the amount of matching sets or pairs of socks , find the probability mass function of variable X. Also give the moment-generating function of X and utilize it to find the mean and variance of X
Expert Solution
steps

Step by step

Solved in 4 steps with 15 images

Blurred answer
Recommended textbooks for you
A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability
A First Course in Probability
Probability
ISBN:
9780321794772
Author:
Sheldon Ross
Publisher:
PEARSON