Question Solved1 Answer 2. Show the following property holds for any random variable X: Var(X) = E(X2) - u. 3. Show the following property holds for any random variables X, Y and V and any constants a, b and c: Cov(a + bx + cV,Y) = boxy + covy.
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Transcribed Image Text: 2. Show the following property holds for any random variable X: Var(X) = E(X2) - u. 3. Show the following property holds for any random variables X, Y and V and any constants a, b and c: Cov(a + bx + cV,Y) = boxy + covy.
More Transcribed Image Text: 2. Show the following property holds for any random variable X: Var(X) = E(X2) - u. 3. Show the following property holds for any random variables X, Y and V and any constants a, b and c: Cov(a + bx + cV,Y) = boxy + covy.
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Let x be any random variable{:[Var(x)=E(x-E(x))^(2)],[var(x)=E(x^(2)+(E(x))^(2)-2xE(x))],[=E(x^(2))+E(E(x))^(2)-2E(x)E(x)],[=E(x^(2))+(E(x))^(2)-2(E(x))^(2)],[=E(x^(2))-(E(x))^(2)],[var(x)=E(x^(2))-mux^(2)]:}quad cov(a+bx+cv,y){:[cov(a+bx+cv","y)],[=b cov(x","y) ... See the full answer