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StatisticsQ&A LibraryMy 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?Question

Asked Sep 26, 2019

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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 |

- Compute 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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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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