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Chapter 4: Q.4.37 (page 166)

Find Var(X) and Var(Y) for X and Y as given in Problem 4.21

Short Answer

Expert verified

In the given information the answers areVarX=80.92,VarY=84.5

Step by step solution

01

Step 1:Given Information

Varx=EX2-EX2

02

Step 2:Calculation

By using the result d\from problem 22 and same notation, we can compute the variance using the identity Var鈦�(X)=EX2鈭�E(X)2.

Now we have that

EX2=402路40148+332路33148+252路25148+502路50148=1625.42

Then we have that,

Var(X)=EX2-E(X)2=1625.42-39.32=80.92

Similarly for Y,

EY2=402路14+332路14+252路14+502路14=1453.5

Now, we have that

Var(Y)=EY2-E(Y)2=1453.5-372=84.5
03

Step 3:Final Answer

The value ofVar(X)=80.92,Var(Y)=84.5

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