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 Sx² + ² ,0 < x < 1,0 < y < 2, f(x, y) = 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 = 12). h. Find P(X> ½ | Y = 1). 1. Determine if the random variables are statistically independent.
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 Sx² + ² ,0 < x < 1,0 < y < 2, f(x, y) = 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 = 12). h. Find P(X> ½ | Y = 1). 1. Determine if the random variables are statistically independent.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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
![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 +
f(x, y) =
:{x²
.xy,0 < x < 1,0 < y < 2,
elsewhere.
3
0,
a. Verify if it is a valid density function.
b.
Find P[(X, Y) E A], where A = {(x, y) | 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(xv).
Find the conditional density f(y\x).
f.
g. Find P(Y> 1 | X = ½).
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%2F937962fc-e091-46b6-93b3-b806a597fb1d%2F8134aae5-76a4-4902-a460-9981d995c346%2F604dllp_processed.png&w=3840&q=75)
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
x² +
f(x, y) =
:{x²
.xy,0 < x < 1,0 < y < 2,
elsewhere.
3
0,
a. Verify if it is a valid density function.
b.
Find P[(X, Y) E A], where A = {(x, y) | 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(xv).
Find the conditional density f(y\x).
f.
g. Find P(Y> 1 | X = ½).
h.
Find P(X> ½ | Y = 1).
i.
Determine if the random variables are statistically independent.
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