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 11X = 12). g. h. Find P(X> 1 Y = 1). i. 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 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 11X = 12). g. h. Find P(X> 1 Y = 1). i. Determine if the random variables are statistically independent.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.3: The Addition And Subtraction Formulas
Problem 76E
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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
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0e2bee5b-7171-40d5-b4b0-fb3b094cde77%2F8f34ca1a-deb3-4d96-8754-99fe7aa4fd80%2Foggr8g_processed.jpeg&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
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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