1. Consider the following continuous Joint PDF. x f(x,y) = K. In ½ < x < y and 1 < y < 2 a. Sketch the region where the PDF lies. b. Find the value of the constant K that makes this a valid joint probability density function c. Find the marginal density function of Y. d. Find the Expectation of Y.

1. Consider the following continuous Joint PDF. x f(x,y) = K. In ½ < x < y and 1 < y < 2 a. Sketch the region where the PDF lies. b. Find the value of the constant K that makes this a valid joint probability density function c. Find the marginal density function of Y. d. Find the Expectation of Y.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.CR: Chapter 13 Review

Problem 52CR

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Question

The use of TI84 plus functions IS allowed, please show the steps/functions on the calculator used to solve this problem, I really appreciate it thank you.

1. Consider the following continuous Joint PDF.
x
f(x,y) = K.
In ½ < x < y and 1 < y < 2
a. Sketch the region where the PDF lies.
b. Find the value of the constant K that makes this a valid joint probability density
function
c. Find the marginal density function of Y.
d. Find the Expectation of Y.

Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.

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