The joint pmf of X and Y is f (x, y) = 1/6, 0 ?x + y ? 2,

Chapter 4, Problem 6E

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QUESTION:

PROBLEM 6E

The joint pmf of X and Y is f (x, y) = 1/6, 0 ≤x + y ≤ 2, where x and y are nonnegative integers.

(a) Sketch the support of X and Y.

(b) Record the marginal pmfs fX(x) and fY(y) in the “margins.”

(c) Compute Cov(X,Y).

(d) Determine ρ, the correlation coefficient.

(e) Find the best-fitting line and draw it on your figure.

Questions & Answers

QUESTION:

PROBLEM 6E

The joint pmf of X and Y is f (x, y) = 1/6, 0 ≤x + y ≤ 2, where x and y are nonnegative integers.

(a) Sketch the support of X and Y.

(b) Record the marginal pmfs fX(x) and fY(y) in the “margins.”

(c) Compute Cov(X,Y).

(d) Determine ρ, the correlation coefficient.

(e) Find the best-fitting line and draw it on your figure.

ANSWER:

Answer

Step 1 of  8

a) Construct a table for a given pmf        0

     

y x

0

1

2

0

1/6

1/6

1/6

3/6

1

1/6

1/6

0

2/6

2

1/6

0

0

1/6

3/6

2/6

1/6

1


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