E[X2 | X1 = 0.3]=? Var(X2 | X1 = 0.3)=?
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 23E
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Solution for c and d?
![Let X, and X, be two continuous random variables with the following joint probability
density function:
f(x1, x2) = {0,
[3x2 ,
0 < x1 < x2 < 1
otherwise
a. Find the marginal density function fx, (x1) of X1.
b. Given that X, is 0.3, what is the probability that X2 is less than 0.5?
c. E[X, | X1 = 0.3]=?
d. Var(X, | X1 = 0.3)=?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8f4c4228-baea-4c29-a8ac-0203ebf95e6b%2F498f63da-cb29-4002-a52f-cfb83a2a6e6c%2Fgihdzu3_processed.png&w=3840&q=75)
Transcribed Image Text:Let X, and X, be two continuous random variables with the following joint probability
density function:
f(x1, x2) = {0,
[3x2 ,
0 < x1 < x2 < 1
otherwise
a. Find the marginal density function fx, (x1) of X1.
b. Given that X, is 0.3, what is the probability that X2 is less than 0.5?
c. E[X, | X1 = 0.3]=?
d. Var(X, | X1 = 0.3)=?
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