Consider the probability distribution function of X and Y as shown. Find P(X>Y) f(x, y) = 12 (2² + xy), 0 < x < 1, 0 < y < 1. ||

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 10E
Question

answer the following and provide precise and complete solution

Consider the probability distribution function of X and Y as shown. Find
P(X>Y)
12
f(x, y) = #(x² + xy), 0 <x < 1, 0 <y< 1.
||
7
3/14
9/14
1
O 5/14
Urn 1 contains 5 white balls and 7 black balls. Urn 2 contains 3 whites and
12 black. A fair coin is flipped; if it is Heads, a ball is drawn from Urn 1, and
if it is Tails, a ball is drawn from Urn 2. Suppose that this experiment is
done and you learn that a white ball was selected. What is the probability
that this ball was in fact taken from Urn 2? (i.e., that the coin flip was Tails)
12/37
25/37
3/15
1/2
Transcribed Image Text:Consider the probability distribution function of X and Y as shown. Find P(X>Y) 12 f(x, y) = #(x² + xy), 0 <x < 1, 0 <y< 1. || 7 3/14 9/14 1 O 5/14 Urn 1 contains 5 white balls and 7 black balls. Urn 2 contains 3 whites and 12 black. A fair coin is flipped; if it is Heads, a ball is drawn from Urn 1, and if it is Tails, a ball is drawn from Urn 2. Suppose that this experiment is done and you learn that a white ball was selected. What is the probability that this ball was in fact taken from Urn 2? (i.e., that the coin flip was Tails) 12/37 25/37 3/15 1/2
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