An evaluation score X1 of a candidate using method 1 has a mean of 100 and a standard deviation of 12, while an evaluation score X2 of a candidate using method 2 has a mean of 100 and a standard deviation of 13. If the two evaluation scores are independent, what values of c1 and c2 can be chosen so that the combined score Y =c1X1 +c2X2 has a mean of 100 and a standard deviation of 10?

Lecture 7 Nicole Rubenstein September 19, 2017 6 Notes on topics from last lecture 2 2 2 Say we have Y = aX + b;E[X] = ▯;V ar(X) = ▯ . Then we know E[Y ] = a▯ + b and V ar(Y ) = a ▯ . Another way to compute variance: 2 2 V ar(X) = E(X ) ▯ [E(X)] 2 2 2 Here, E(X ) is the second moment of X and [E(X)] is the mean squared. If you can compute E(X ), this is typically a much easier way to ▯nd the variance. Proof.