Answered: a. Find the marginal densities of X and…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 22PFA

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1. We have a pair of dice each with six sides all numbered 1-6. One of them is blue the other white. The dice are rolled. Let X be the number shown on top of the blue die and Y be the sum of the numbers shown on the top sides of the blue and white dice.

a. Find the marginal densities of X and Y.

b. Are X and Y independent?

c. Find the st. deviation of Y.

d. Find the covariance of X and Y?

Definition Definition Measure of how two random variables change together. Covariance indicates the joint variability or the directional relationship between two variables. When two variables change in the same direction (i.e., if they either increase or decrease together), they have a positive covariance. When the change is in opposite directions (i.e., if one increases and the other decreases), the two variables have a a negative covariance.

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