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Q1. Joint distribution of discrete random variables Toss a fair coin 3 times. Let X be the total number of “head"s in the 3 tosses. Let Y be the indicator of "head" in the 1st toss. (That is, if the 1st toss is “head", then Y = 1, otherwise Y = 0. ) 1. Find the joint distribution f(x, y) of X and Y. 2. Find the marginal distribution fx() of X and the marginal distribution fy (y) of Y. 3. Are X and Y independent? Justify your answer.

Q1. Joint distribution of discrete random variables Toss a fair coin 3 times. Let X be the total number of “head"s in the 3 tosses. Let Y be the indicator of "head" in the 1st toss. (That is, if the 1st toss is “head", then Y = 1, otherwise Y = 0. ) 1. Find the joint distribution f(x, y) of X and Y. 2. Find the marginal distribution fx() of X and the marginal distribution fy (y) of Y. 3. Are X and Y independent? Justify your answer.

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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just the subparts 1,2 and 3 please thank you so much

Q1. Joint distribution of discrete random variables Toss a fair coin 3 times. Let X be the total number of “head"s in the 3 tosses. Let Y be the indicator of “head" in the 1st toss. (That is, if the 1st toss is “head", then Y = 1, otherwise Y = 0. ) 1. Find the joint distribution f(r, y) of X and Y. 2. Find the marginal distribution fx(x) of X and the marginal distribution fy (3) of Y. 3. Are X and Y independent? Justify your answer. 4. Calculate the expected values E(X), E(Y) and the variances Var(X), Var(Y). 5. Calculate the covariance Cov(X, Y) of X and Y. Hint: Use definition Coo (X, Y) - E(X- E(X)(Υ - E(Υ))] = ΣΣα- ΕX)) (y - E(Υ))f(x, y).
Transcribed Image Text:Q1. Joint distribution of discrete random variables Toss a fair coin 3 times. Let X be the total number of “head"s in the 3 tosses. Let Y be the indicator of “head" in the 1st toss. (That is, if the 1st toss is “head", then Y = 1, otherwise Y = 0. ) 1. Find the joint distribution f(r, y) of X and Y. 2. Find the marginal distribution fx(x) of X and the marginal distribution fy (3) of Y. 3. Are X and Y independent? Justify your answer. 4. Calculate the expected values E(X), E(Y) and the variances Var(X), Var(Y). 5. Calculate the covariance Cov(X, Y) of X and Y. Hint: Use definition Coo (X, Y) - E(X- E(X)(Υ - E(Υ))] = ΣΣα- ΕX)) (y - E(Υ))f(x, y).
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