Question

Let X be a random variable that takes values -2, -1, 0, 1, 2; cach with probability 1/5. Let Y = X2. (a) Find the joint distribution of X and Y. (Providing a joint pmf table is enough.) (b) Show X and Y are not independent but Cov(X,Y) = 0. This is an example of uncorrelated but non-independent random variables.

Name: let x be a random variable that takes values 2 1 0 1 2 cach with probability 15 let y x2 a find the joint distribution of x and y providing a joint pmf table is enough b show x and y are not independe
Uploaded: 2023-09-07T07:18:31-08:00
Duration: 4 min 3 s
Channel: Jacob Fry
Description: let x be a random variable that takes values 2 1 0 1 2 cach with probability 15 let y x2 a find the joint distribution of x and y providing a joint pmf table is enough b show x and y are not independe

          Let X be a random variable that takes values -2, -1, 0, 1, 2; cach with
probability 1/5. Let Y = X2. (a) Find the joint distribution of X and Y. (Providing a joint pmf table is enough.) (b) Show X and Y are not independent but Cov(X,Y) = 0. This is an example of uncorrelated but non-independent random variables.

Added by G M.

Mathematical Statistics with Applications

Dennis D. Wackerly, William Mendenhall… 7th Edition

Chapter 5

Instant Answer

Solved by Expert Jacob Fry

09/07/2023

Step 1

| | Y=0 | Y=1 | Y=4 | |---|-----|-----|-----| | X=-2 | 0 | 0 | 1/5 | | X=-1 | 0 | 1/5 | 0 | | X=0 | 1/5 | 0 | 0 | | X=1 | 0 | 1/5 | 0 | | X=2 | 0 | 0 | 1/5 | (b) To show that X and Y are not independent, we need to find an example where Show more…

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Let X be a random variable that takes values -2, -1, 0, 1, 2; cach with probability 1/5. Let Y = X2. (a) Find the joint distribution of X and Y. (Providing a joint pmf table is enough.) (b) Show X and Y are not independent but Cov(X,Y) = 0. This is an example of uncorrelated but non-independent random variables.