3. Show that the following function satisfies the properties of a joint probability mass functionfxy(x, y)Y- 1.0- 2bo1-0.5-10.51.1.1.013.1 Marginal probability distribution of X3.2 Conditional probability distribution of Y given that X = 13.3 Conditional probability distribution of X given that Y =13.4 Are X and Y independent?2.

As per our guidelines we can solve first three sub part of question and rest can be reposted.…

Answered: Show that the following function…

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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Suppose that two continuous random variables X and Y have a joint probability densityfunction f(x, y) = A(x − 3)y for -2≤x≤3 and 4≤y≤6a) What is the value of A?b) What is P(0≤x≤1 and 4≤y≤5)?c) Construct the marginal probability density functions.d) Are the random variables X and Y independent?e) If Y = 5, what is the conditional probability density function of X?f) What are the expectations and variances of the random variables X and Y ?g) What is the covariance of X and Y?h) What is the correlation between X and Y?
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3.76 Consider the situation of Review Exercise 3.75. But suppose the joint distribution of the two proportions is given by f(x1, x2) = 6x2, 0 < x2 < x1 < 1, 0, elsewhere. (a) Give the marginal distribution fX1 (x1) of the proportion X1 and verify that it is a valid density function. (b) What is the probability that proportion X2 is less than 0.5, given that X1 is 0.7?.
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