QUESTION 2 Two random variables X and Y have the following joint probability density function. f(x, y) = ('/k) x²ye*+ y) , x > 0, y > 0. (i) Determine the value of the constant k. Determine the joint moment generating function of the two random variables. Using your answer to (ii), determine the covariance of X and Y. What can you say about (ii) (iii) these random variables? (iv) Determine the variance of the random variable X.
QUESTION 2 Two random variables X and Y have the following joint probability density function. f(x, y) = ('/k) x²ye*+ y) , x > 0, y > 0. (i) Determine the value of the constant k. Determine the joint moment generating function of the two random variables. Using your answer to (ii), determine the covariance of X and Y. What can you say about (ii) (iii) these random variables? (iv) Determine the variance of the random variable X.
MATLAB: An Introduction with Applications
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![QUESTION 2
Two random variables X and Y have the following joint probability density function.
f(x, y) = (/k) x²ye-(x*+ y) , x > 0, y > 0.
(i)
Determine the value of the constant k.
(ii)
Determine the joint moment generating function of the two random variables.
(ii)
Using your answer to (ii), determine the covariance of X and Y. What can you say about
these random variables?
(iv)
Determine the variance of the random variable X.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0e0385d0-6f78-4ba4-9c0f-db0e524e6434%2F81ef4432-18fc-4d45-b786-d02b1ee2127d%2F3rba3_processed.png&w=3840&q=75)
Transcribed Image Text:QUESTION 2
Two random variables X and Y have the following joint probability density function.
f(x, y) = (/k) x²ye-(x*+ y) , x > 0, y > 0.
(i)
Determine the value of the constant k.
(ii)
Determine the joint moment generating function of the two random variables.
(ii)
Using your answer to (ii), determine the covariance of X and Y. What can you say about
these random variables?
(iv)
Determine the variance of the random variable X.
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