Question

An instructor has given a short quiz consisting of two parts. For a randomly selected student, let X = the number of points earned on the first part and Y = the number of points earned on the second part. Suppose that the joint pmf of X and Y is given in the accompanying table.

		y
p(x, y)		0	5	10	15
x	0	0.03	0.06	0.02	0.10
	5	0.04	0.16	0.20	0.10
	10	0.01	0.15	0.12	0.01

(a) Compute the covariance for X and Y. (Round your answer to two decimal places.)
Cov(X, Y) =

(b) Compute ρ for X and Y. (Round your answer to two decimal places.)
ρ =

Answer 1

An instructor has given a short quiz consisting of two parts. For a randomly selected student, let X = the number of points earned on the first part and Y = the number of points earned on the second part. Suppose that the joint pmf of X and Y is given in the accompanying table.

		y
p(x, y)		0	5	10	15	Total
x	0	0.03	0.06	0.02	0.10	0.21
	5	0.04	0.16	0.20	0.10	0.50
	10	0.01	0.15	0.12	0.01	0.29
Total		0.08	0.37	0.34	0.21	1.00

(a)

We want to compute the Covariance for X and Y.

Covariance for X and Y is given by the formula,

Cov(X,Y)=E(XY) - E(X)E(Y)

Now Cov(X,Y) is given by,

=> Cov(X,Y)=E(XY) - E(X)E(Y)

Answer:- Cov(X,Y)= - 2.86

(b)

Now we want to compute correlation coefficient for X and Y.

Correlation Coefficient for X and Y is given by the formula,

Answer:- Correlation Coefficient = - 0.18 [Round to two decimal places.]