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 joint pmf of X and Y is given in the accompanying table. the number of points earned on the second part. Suppose that the 0.02 0.04 100.01 0.15 10 0.02 0.20 0.15 15 0.10 0.10 0.01 0.06 0.14 (a) Compute the covariance for X and Y. (Round your answer to two decimal places.) Cov(X, Y) (b) Compute p for X and Y (Round your answer to two decimal places.)

Answer 1

X	P(X=x)
0	0.2
5	0.48
10	0.32

Y	P(Y=y)
0	0.07
5	0.35
10	0.37
15	0.21

XY	P(XY=xy)
0	0.25
25	0.14
50	0.35
75	0.10
100	0.15
150	0.01

$\small Cov(X,Y)=E(XY)-E(X)E(Y)=45 - 5.45*8.6=-3.16$

$\small \\\rho(X,Y)=cov(X,Y)/sd(X)sd(Y)= -3.16/(3.5552*4.3634)= -0.2036\simeq -0.20$