2.5.4A fair coin is tossed four times, and the random variable X is the number of heads in the first three tosses and the random variable Yis the number of heads in the last three tosses. (a) What is the joint probability mass function of X and Y? (b) What are the marginal probability mass functions of X and Y? (c) Are the random variables X and Yindependent? (d) What are the expectations and variances of the random variables X and Y? (e) What is the covariance of X and Y? (f) If there is one head in the last three tosses, what is the conditional probability mass function of X? What are the conditional expectation and variance of X?

2.5.4A fair coin is tossed four times, and the random variable X is the number of heads in the first three tosses and the random variable Yis the number of heads in the last three tosses. (a) What is the joint probability mass function of X and Y? (b) What are the marginal probability mass functions of X and Y? (c) Are the random variables X and Yindependent? (d) What are the expectations and variances of the random variables X and Y? (e) What is the covariance of X and Y? (f) If there is one head in the last three tosses, what is the conditional probability mass function of X? What are the conditional expectation 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...

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