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Chapter 7: Q.22 (page 360)

Show that Y=a+bX, then

蚁(X,Y)=+1鈥呪赌呪赌呪赌�ifb>0鈭�1鈥呪赌呪赌呪赌�ifb<0

Short Answer

Expert verified

We prove that

Y=a+bX

Step by step solution

01

Given information

Given in the question that, We have to find

Show that Y=a+bX.

02

Explanation

If Y=a+bXwith parameters aand b

蚁(X,Y)=Cov鈦�(X,Y)Var鈦�(X)Var鈦�(Y)

Cov(X,Y)=Cov(X,a+bX)

Var(Y)=Var(a+bX)

=o+b2Var(X)

Now,

蚁(X,Y)=bVar鈦�(X)Var鈦�(X)b2Var鈦�(X)

Finally,

蚁(X,Y)=+1鈥呪赌呪赌呪赌�ifb>0鈭�1鈥呪赌呪赌呪赌�ifb<0

03

Final answer

We prove that

Y=a+bX

and

蚁(X,Y)=+1鈥呪赌呪赌呪赌�ifb>0鈭�1鈥呪赌呪赌呪赌�ifb<0

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Most popular questions from this chapter

An urn contains 30balls, of which10are red and 8 are blue. From this urn, 12 balls are randomly withdrawn. Let X denote the number of red and Y the number of blue balls that are withdrawn. Find Cov(X, Y)

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