2. Two discrete random variables X and Y have the joint PMF given byx = 1, y = 1= 1, y = 20.1 x = 2, y = 1Рxr(х, у) 3D { 0.2 х%3D2,у%3D20.1 x = 3, y = 10.3 х%3D 3, у — 20 otherwise(0.20.1X =Determine the following:a) The marginal PMFS of X and Y (i.e., px(x) and py (y))b) The conditional PMF of X given Y,Px|y (x|y)c) Whether X and Y are independent.

It is an important part of statistics. It is widely used.

2. Two discrete random variables X and Y have the joint PMF given by 0.2 х 3D 1,у %3D 1 0.1 x = 1, y = 2 х%3D 2, у %3D 1 x = 2, y = 2 0.1 0.1 Pxy(x, y) = {0.2 x = 3, y = 1 0.3 x = 3, y = 2 otherwise Determine the following: a) The marginal PMFS of X and Y (i.e., px(x) and py(y)) b) The conditional PMF of X given Y, px|y (x|y) c) Whether X and Y are independent.

2. Two discrete random variables X and Y have the joint PMF given by 0.2 х 3D 1,у %3D 1 0.1 x = 1, y = 2 х%3D 2, у %3D 1 x = 2, y = 2 0.1 0.1 Pxy(x, y) = {0.2 x = 3, y = 1 0.3 x = 3, y = 2 otherwise Determine the following: a) The marginal PMFS of X and Y (i.e., px(x) and py(y)) b) The conditional PMF of X given Y, px|y (x|y) c) Whether X and Y are 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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5. Suppose Y₁, Y2,..., Y are independent random variables whose density is for y0 for some > 0. (a) Show that the MLE for is f(y) = 30y²e-04³ n ÔMLE = ΣΤ (b) Use the R code to estimate the bias and the variance when n = 20 and 0 = 2.
Please show step by step explanations. Thank you.
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