Hi all, Am a little confused here, please can someone help? in the solutions the variance is given by 3*100^2+4*300^2 however, I would have thought it would be 3^2*100^2+4^2*300^2, as is the case with the example on page 195 for 2X-Y. Please can someone explain this, in my head we are working out 3X-4Y , I just don’t understand why the coefficients aren’t being squared for the variance part. Thanks
Hi Molly In Practice Question 4.7 we are looking at the next four home insurance claims and next three car insurance claims, each claim is normally distributed and independent, we are looking at each claim separately. Looking at the house insurance claims, which are represented by a random variable Y, it would be Y1, Y2, Y3 and Y4, they each have a normal distribution, this is not the same as the distribution of 4Y, so it is just 4*300^2 for the variance. In Section 4.2 you were asked to determine the distribution of 2X-Y, so the coefficients were squared. Hope this helps explain the difference.
