Let x denote the size of a bodily injury claim and y denote the size of the corresponding property damage claim. let z1 = x + y. from prior experience we know var(x) = 144, var(y) = 64 and var(x + y) = 308. it is expected that bodily injury claims will rise 10% next year and property damage will rise by a fixed amount of 5. let z2 be the new trial of bodily injury and property damage. compute cov(z1, z2 ).

Step-by-step explanation:

Data given:

Var(X) = 144, Var(Y) = 64 and Var(X + Y) = 308

We have defined the following random variable:

And if we find the variance for Z1 we got:

If we solve for the we got:

And replacing the values that we have we got:

Now we define the new random variable like this:

And we are interested on find the following covariance:

And if we apply properties of covariance we have this:

We know that if a is a constant and X,Y random variables , and , , so then using these properties we got:

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