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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

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 31E
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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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