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d. Find the marginal density h(y). e. Find the conditional density f(xly). f. Find the conditional density f (ylx).

d. Find the marginal density h(y). e. Find the conditional density f(xly). f. Find the conditional density f (ylx).

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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d, e, f
Let X denote the reaction time, in seconds, to a certain stimulus and Y denote the temperature (°F) at which a certain reaction starts to take place. Suppose that two random variables X and Y have the joint density xy f(x, y) = ={*x². +3,0 < x < 1,0 < y < 2, elsewhere. 0, a. Verify if it is a valid density function. b. Find P[(X, Y) € A], where A = {(x, y) 1 0<x< ½, ¼ <y<½. c. Find the marginal density g(x). d. Find the marginal density h(y). e. Find the conditional density f(xly). f. Find the conditional density f(ylx). Find P(Y> 11X = 12). g. h. Find P(X> 1 Y = 1). i. Determine if the random variables are statistically independent.
Transcribed Image Text:Let X denote the reaction time, in seconds, to a certain stimulus and Y denote the temperature (°F) at which a certain reaction starts to take place. Suppose that two random variables X and Y have the joint density xy f(x, y) = ={*x². +3,0 < x < 1,0 < y < 2, elsewhere. 0, a. Verify if it is a valid density function. b. Find P[(X, Y) € A], where A = {(x, y) 1 0<x< ½, ¼ <y<½. c. Find the marginal density g(x). d. Find the marginal density h(y). e. Find the conditional density f(xly). f. Find the conditional density f(ylx). Find P(Y> 11X = 12). g. h. Find P(X> 1 Y = 1). i. Determine if the random variables are statistically independent.
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