Math

StatisticsSTATISTICS F/BUSINESS+ECONOMICS-TEXTGiven below is a bivariate distribution for the random variables x and y . f ( x , y ) x y .2 50 80 .5 30 50 .3 40 60 a. Compute the expected value and the variance for x and y . b. Develop a probability distribution for x + y . c. Using the result of part (b), compute E ( x + y ) and Var ( x + y ). d. Compute the covariance and correlation for x and y . Are x and y positively related, negatively related, or unrelated? e. Is the variance of the sum of x and y bigger, smaller, or the same as the sum of the individual variances? Why?BuyFind*arrow_forward*

13th Edition

Anderson

Publisher: CENGAGE L

ISBN: 9781305881884

Chapter 5.4, Problem 25E

Textbook Problem

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

f(x, y) |
x |
y |

.2 | 50 | 80 |

.5 | 30 | 50 |

.3 | 40 | 60 |

- a. Compute the expected value and the variance for
*x*and*y*. - b. Develop a probability distribution for
*x*+*y*. - c. Using the result of part (b), compute
*E*(*x + y*) and*Var*(*x*+*y*). - d. Compute the covariance and correlation for
*x*and*y*. Are*x*and*y*positively related, negatively related, or unrelated? - e. Is the variance of the sum of
*x*and*y*bigger, smaller, or the same as the sum of the individual variances? Why?

STATISTICS F/BUSINESS+ECONOMICS-TEXT

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