Problem 1: A random variable X whose probability density function is given by fx(x) = 0.38(x-2)+ k tri (x²). Another random variable Yis related to X through Y= 2X-3. Find 1. The value of k 2. The expected value and the variance of X 3. The probability density function of Y. Problem 2: DRV X and Y have PDFs as fx(x) = 0.28(x) + 0.58(x-4) + 0.38(x-6) fy(y) = 0.58(x + 1) + 0.58(x-1) 1. What are the expected values E[X] and E[Y]? 2. What are the variances σ and o? 3. Assume a random variable Z = X + Y, what is the PDF of the random variable Z.
Problem 1: A random variable X whose probability density function is given by fx(x) = 0.38(x-2)+ k tri (x²). Another random variable Yis related to X through Y= 2X-3. Find 1. The value of k 2. The expected value and the variance of X 3. The probability density function of Y. Problem 2: DRV X and Y have PDFs as fx(x) = 0.28(x) + 0.58(x-4) + 0.38(x-6) fy(y) = 0.58(x + 1) + 0.58(x-1) 1. What are the expected values E[X] and E[Y]? 2. What are the variances σ and o? 3. Assume a random variable Z = X + Y, what is the PDF of the random variable Z.
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.
Chapter1: Functions
Section1.2: The Least Square Line
Problem 1E
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![Problem 1:
A random variable X whose probability density function is given by
fx(x) = 0.38(x-2)+ k tri (x²).
Another random variable Yis related to X through Y= 2X-3. Find
1. The value of k
2. The expected value and the variance of X
3. The probability density function of Y.
Problem 2:
DRV X and Y have PDFs as
fx(x) = 0.28(x) + 0.58(x-4) + 0.38(x-6)
fy(y) = 0.58(x + 1) + 0.58(x-1)
1. What are the expected values E[X] and E[Y]?
2. What are the variances σ and o?
3. Assume a random variable Z = X + Y, what is the PDF of the random variable Z.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdf80eb80-4b91-4edb-8819-5ed39035b7a8%2F65f0cb9b-98d4-49ac-bede-bd51d45b017b%2Fy326ss_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem 1:
A random variable X whose probability density function is given by
fx(x) = 0.38(x-2)+ k tri (x²).
Another random variable Yis related to X through Y= 2X-3. Find
1. The value of k
2. The expected value and the variance of X
3. The probability density function of Y.
Problem 2:
DRV X and Y have PDFs as
fx(x) = 0.28(x) + 0.58(x-4) + 0.38(x-6)
fy(y) = 0.58(x + 1) + 0.58(x-1)
1. What are the expected values E[X] and E[Y]?
2. What are the variances σ and o?
3. Assume a random variable Z = X + Y, what is the PDF of the random variable Z.
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