Let X and Y have the joint pmf defined by f(0, 0) = f(1, 2) = 0.2, f(0, 1) = f(1, 1) =

Chapter 4, Problem 4.2-2

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QUESTION:

Let X and Y have the joint pmf defined by f(0, 0) = f(1, 2) = 0.2, f(0, 1) = f(1, 1) = 0.3.

(a) Depict the points and corresponding probabilities on a graph.

(b) Give the marginal pmfs in the “margins.” (c) Compute \(\mu_{X}, \mu_{Y}, \sigma_{X}^{2}, \sigma_{Y}^{2}, \operatorname{Cov}(X, Y)\), and \(\rho\).

(d) Find the equation of the least squares regression line and draw it on your graph. Does the line make sense to you intuitively?

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QUESTION:

Let X and Y have the joint pmf defined by f(0, 0) = f(1, 2) = 0.2, f(0, 1) = f(1, 1) = 0.3.

(a) Depict the points and corresponding probabilities on a graph.

(b) Give the marginal pmfs in the “margins.” (c) Compute \(\mu_{X}, \mu_{Y}, \sigma_{X}^{2}, \sigma_{Y}^{2}, \operatorname{Cov}(X, Y)\), and \(\rho\).

(d) Find the equation of the least squares regression line and draw it on your graph. Does the line make sense to you intuitively?

ANSWER:

Step 1 of 5

Given that,

The X and Y are two random variables.

The joint pmf of x and Y are defined by  and  

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