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select a point (X,Y) from the triangle {(x,) : x,y \in {1,2,...,6}, y <= x} in the following nonuniform way. "First, select X discrete uniformly from {1,2,...,6}. Then, given X=x, select Y discrete uniformly from {1,...,x}. " a) Find the joint pmf of (X,Y) b) Find the margin

select a point (X,Y) from the triangle {(x,) : x,y \in {1,2,...,6}, y <= x} in the following nonuniform way. "First, select X discrete uniformly from {1,2,...,6}. Then, given X=x, select Y discrete uniformly from {1,...,x}. " a) Find the joint pmf of (X,Y) b) Find the margin

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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We randomly select a point (X,Y) from the triangle {(x,) : x,y \in {1,2,...,6}, y <= x} in the following nonuniform way. "First, select X discrete uniformly from {1,2,...,6}. Then, given X=x, select Y discrete uniformly from {1,...,x}. "

a) Find the joint pmf of (X,Y)

b) Find the marginal pmfs of X and Y

c) Find the conditional pmf of X given Y = 2.

d) Write R-code that simulates 10^4 pairs (X,Y) and use the table() command to to check if your results of a) b) and c) are correct.

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