# My last question I mixed the data and the question, my bad!5) Given below is a bivariate distribution for the random variables x and y.f(x, y)xy0.250800.530500.34060Compute the expected value and the variance for x and y.Develop a probability distribution for x + y.Using the result of part (b), compute E(x + y) and Var(x + y).Compute the covariance and correlation for x and y. Are x and y positively related, negatively related, or unrelated?Is the variance of the sum of x and y bigger, smaller, or the same as the sum of the individual variances? Why?

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My last question I mixed the data and the question, my bad!

5) Given below is a bivariate distribution for the random variables x and y.

 f(x, y) x y 0.2 50 80 0.5 30 50 0.3 40 60
1. Compute the expected value and the variance for x and y.
2. Develop a probability distribution for x + y.
3. Using the result of part (b), compute E(x + y) and Var(x + y).
4. Compute the covariance and correlation for x and y. Are x and y positively related, negatively related, or unrelated?
5. Is the variance of the sum of x and y bigger, smaller, or the same as the sum of the individual variances? Why?
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Step 1

Note:

Hi! Thank you for posting the question. Since your question has more than 3 parts, we have solved the first 3 parts for you. If you need help with any of the other parts, please re-post the question and mention the part you need help with.

Step 2

The marginal density function of X is obtained as follows:

Step 3

1. Finding the expected value and the variance of X and Y:

The expected value and the variance of X are 37...

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