Bhmut Answerl SeeProgresal Practice Another Version An instructor has given a sh
ID: 3325302 • Letter: B
Question
Bhmut Answerl SeeProgresal Practice Another Version An instructor has given a short quiz consisting of two parts. For a randomly selected student, let X -the number of points eaned on the first part and Y- the number of points earned on the second pa Suppose that the joint pmf of X and Y is given in the accompanying table. p(x,y) 0 5 10 15 0d030.06 0.02 0.10 x 5 0.04 0.140.20 0.10 10 0.01 0.15 0.14 0.01 (a) Compute the covariance for X and y (Round your answer to two decimal places.) (b) Compute p for X and (Round your answer to two decimal places. Need Help? 7 5Explanation / Answer
Solution
E(X) = 0*0.21+5*0.48+10*0.31=5.5
V(X) = E(X2)-(E(X)))2
V(X) = 0+25*0.48+100*0.31 - (5.5)2 = 43-(5.5)2 = 12.75
E(Y) = 0*0.08+5*0.35+10*0.36+15*0.21 = 8.5
V(Y) = 0+25*0.35+100*0.36+225*0.21 - (8.5)2 = 19.75
E(XY) = 0+25*0.14+50*0.35+75*0.1+100*0.14+150*0.01 = 44
(a) COV(X,Y) = E(XY)-E(X)E(Y) = 44 - (5.5)(8.5) = -2.75
(b) Correlation = COV(X,Y)/s(X)s(Y)
= -2.75/(12.75)0.5(19.75)0.5 = -0.17
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