5.1.9 WP SS vs Determine the value of c such that thefunction f(x, y) = cxy for 0 < x <3 and 0 < y < 3 satisfies theproperties of a joint probability density function. Determine thefollowing:a. P(X < 2, Y <3)c. P(1 1.8, 1

The given joint density function is,“Since you have posted a question with multiple sub parts, we…

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5.1.9 WP SS VS Determine the value of c such that the function f(x, y) = cxy for 0 1.8, 1< Y < 2.5)

A First Course in Probability (10th Edition)

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ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

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Question

5.1.9 WP SS vs Determine the value of c such that the
function f(x, y) = cxy for 0 < x <3 and 0 < y < 3 satisfies the
properties of a joint probability density function. Determine the
following:
a. P(X < 2, Y <3)
c. P(1 <Y <2.5)
e. E(X)
g. Marginal probability distribution of X
b. P(X < 2.5)
d.
f.
P(X> 1.8, 1<Y < 2.5)
P(X <0, Y <4)

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Step 1: Given Information

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Step 2: Computing the value of the constant c

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Step 3: Computing the P(X<2, Y<3)

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Step 4: Computing the P(X<2.5)

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Step 5: Computing the P(1<Y<2.5)

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d. P(X> 1.8, 1 <Y < 2.5)
e. E(X)
f. P(X <0,Y <4)
g. Marginal probability distribution of X

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