Question

In: Statistics and Probability

An instructor has given a short quiz consisting of two parts. For a randomly selected student,...

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 =

Solutions

Expert Solution

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.]


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