QUESTION 6Two discrete independent random variables X and Y can take values 0 and 1 only. Fill in the joint probability distribution table below, knowing the distributions of X and Y given as marginaldistribution over the last row (for X) and last column (for Y).X=0X=1P(Y=y)Y=0 0.10.3Y=1 0.20.4P(X=x)(a) Calculate the marginal distributions of X and Y. (fill in your answer as a number 0.x)(b) What is the probability P(X+Y = 1) =? (fill in your answer as a number 0.x)(c) Are the variables X and Y independent? Input your answer as Y or N here:

X=0 X=1 P(Y=y) Y=0 0.1 0.3 0.4 Y=1 0.2 0.4 0.6 P(X=x) 0.3 0.7 1

Answered: QUESTION 6 Two discrete independent…

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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part 1 of 2 Consider a discrete random variable X that is defined by its piece-wise defined cumulative distribution function: Pr(X < x) 0.8- 0.6(1, 0.5) 0.4 0.2 (4,1) (3, 0.9) -2 -1 0 1 2 3 4 5 6 What is the probability distribution of X? part 2 of 2 Compute the expected value (mean) for X. 1. 2. 3. 4. x 1 3 4 x 1 3 4 x 1 3 4 x 1 3 4 Pr(X = x) 0 0.1 0.4 Pr(X = x) 0.5 0.9 1 Pr(X = x) 0.5 0.4 0.1 Pr(X = x) 10 50 40 1. At least 5.0 2. At least 2.0, but less than 3.0 3. At least 4.0, but less than 5.0 4. At least 3.0, but less than 4.0 5. Less than 2.0
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A fair coin is flipped three times. Let X represent the number of heads to occur on the first two flips and Y the number of heads to occur on the last two flips. (a) Find the joint probability function, along with each marginal function, for X and Y. (b) Find cov(X, Y). (c) Are X and Y independent? Explain your answer. Hint: There are 8 outcomes for this expermient, e.g., if the outcome is HTT, then we have X = 1 and Y = 0.

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