3. Let X be a uniform random variable that takes values -2, -1, 0, 1, 2. Let Y = X²?. Y\X -2 -1 1 2 PY 1 4 Px (a) Fill out the table giving the joint and marginal PMFS for X and Y. (b) Find E[X] and E[Y]. (c) Find the covariance of X and Y.

3. Let X be a uniform random variable that takes values -2, -1, 0, 1, 2. Let Y = X²?. Y\X -2 -1 1 2 PY 1 4 Px (a) Fill out the table giving the joint and marginal PMFS for X and Y. (b) Find E[X] and E[Y]. (c) Find the covariance of X and Y.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter1: Functions

Section1.2: The Least Square Line

Problem 1E

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Fill out the table giving the joint and marginal PMFs for X and Y.

Find E[X] and E[Y].

Find the covariance of X and Y.

Are X and Y independent?

3. Let X be a uniform random variable that takes values -2, -1, 0, 1, 2. Let Y = X².
Y\X
-2
-1
1
2
PY
1
4
Px
(a) Fill out the table giving the joint and marginal PMFs for X and Y.
(b) Find E[X] and E[Y].
(c) Find the covariance of X and Y.
(d) Are X and Y independent? Explain.

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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