Hello all, I came across the example in chapter 15 page 14 and the variance of uniform distribution really got me! I have to admit that I don't have any knowledge of probability at all(also it is one of the subjects that i hated the most!). However, according to the formula of variance, which is S^2=E(X^2)-[E(x)]^2, the answer is 0.0002, which is so different from the result worked out from the "1/12 (b-a)^2" standard formula of variance for uniform distribution. This really worries me a lot since there is a lot of probability distributions out there and I don't know any of the formulas for the mean and variance! Do I have to start memorize all the formulas now in case they will give me a nasty surprise in my coming exam? Thanks in advance for all the advices!
When I do the calculation of the variance using the first principles formula: Var(X)=E(X^2)-(EX)^2 I get exactly the same answer as is given in the Notes using the formula (1/12)*(b-a)^2. So I suspect something's gone amiss for you... However, you do not need to use the first principles formula. You can state the (1/12)*(b-a)^2 formula for the variance and use it. This formula and lots of other useful stuff on statistical distributons e.g. means/variances (and more!) is given in the yellow pages at the front of your Formulae and Tables for Actuarial Examinations book. You will be given one of these in the exam, but they are also invaluable for studying. If you do not have one, you can buy one from the profession's website: http://www.actuaries.org.uk/members/transactions/publications_shop Go to formulae and tables in the left hand column and then you need the second edition. Hope this helps to put your mind at rest.
