2. 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 (x² + 2/2/1,0 < x < 1,0 < y < 2, xy f(x, y) = = {x² ++ 3 elsewhere. 0, a. Verify if it is a valid density function. b. Find P[(X, Y) E A], where A = {(x, y) [ 0 1 | X = ¹½). h. Find P(X> ½ Y = 1). i. Determine if the random variables are statistically independent.
2. 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 (x² + 2/2/1,0 < x < 1,0 < y < 2, xy f(x, y) = = {x² ++ 3 elsewhere. 0, a. Verify if it is a valid density function. b. Find P[(X, Y) E A], where A = {(x, y) [ 0 1 | X = ¹½). h. Find P(X> ½ Y = 1). i. Determine if the random variables are statistically independent.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 12T
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please provide a complete, correct, and detailed solution and answers asap
![2. 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
(x² + 2/2/1,0 < x < 1,0 < y < 2,
xy
f(x, y) = = {x² ++
3
elsewhere.
0,
a. Verify if it is a valid density function.
b. Find P[(X, Y) E A], where A = {(x, y) [ 0<x< ½, ½ <y< ½2.
c. Find the marginal density g(x).
d.
Find the marginal density h(v).
e. Find the conditional density f(xy).
f. Find the conditional density f(x).
g. Find P(Y> 1 | X = ¹½).
h. Find P(X> ½ Y = 1).
i. Determine if the random variables are statistically independent.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa3e0b7e6-cfd4-4a9f-b78d-e377aaf6b3fa%2F170faca7-8b37-4653-88a5-ae0845d1fa20%2F6x6wak_processed.png&w=3840&q=75)
Transcribed Image Text:2. 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
(x² + 2/2/1,0 < x < 1,0 < y < 2,
xy
f(x, y) = = {x² ++
3
elsewhere.
0,
a. Verify if it is a valid density function.
b. Find P[(X, Y) E A], where A = {(x, y) [ 0<x< ½, ½ <y< ½2.
c. Find the marginal density g(x).
d.
Find the marginal density h(v).
e. Find the conditional density f(xy).
f. Find the conditional density f(x).
g. Find P(Y> 1 | X = ¹½).
h. Find P(X> ½ Y = 1).
i. Determine if the random variables are statistically independent.
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