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Let X denote the reaction time, in seconds, toa 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 a.Verify if itis a valid density function. b.Find P[(X, Y) ∈A], where A = {(x, y) | 0 < x < ½, ¼< y < ½. c.Find the marginal density g(x).

Let X denote the reaction time, in seconds, toa 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 a.Verify if itis a valid density function. b.Find P[(X, Y) ∈A], where A = {(x, y) | 0 < x < ½, ¼< y < ½. c.Find the marginal density g(x).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.3: Algebraic Expressions
Problem 32E
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Let X denote the reaction time, in seconds, toa 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

a.Verify if itis a valid density function.
b.Find P[(X, Y) ∈A], where A = {(x, y) | 0 < x < ½, ¼< y < ½.
c.Find the marginal density g(x).
d.Find the marginal densityh(y).
e.Find the conditional densityf(x|y).
f.Find the conditional density f(y|x).
g.Find P(Y > 1|X = ½).
h.Find P(X> ½|Y= 1).
i. Determine if the random variables are statistically independent.

f(x, y) = x² xy ² +3,0 0, ,0 < x < 1,0 <y< 2, elsewhere.
Transcribed Image Text:f(x, y) = x² xy ² +3,0 0, ,0 < x < 1,0 <y< 2, elsewhere.
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