An instructor has given a short quiz consisting of two parts. For a randomly sel

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.

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

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

p(x, y)o 10 0.02 0.20 0.17 15 0.10 0.10 0.01 5 0 0.01 x 50.04 0.13 10 9 0.06 0.01 0.15

Explanation / Answer

for above:

for above joint distribution of X:

and Joint distribution of Y:

a) here E(XY) =46.75

therefore Cov(X, Y) = E(XY)-E(X)*E(Y) =46.75-5.75*8.75=-3.56

b)

= Cov(X,Y)/(Var(X)*Var(Y))1/2 =-0.23

y x 0 5 10 15 Total 0 0.01 0.06 0.02 0.1 0.19 5 0.04 0.13 0.2 0.1 0.47 10 0.01 0.15 0.17 0.01 0.34 Total 0.06 0.34 0.39 0.21 1

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