I hope I am not being silly here - but what formula have they used to calculate the s^2 variance in the example on page 14 of chapter 15? The formulas I know of are 1/n(sum of)(x-mean)^2 or E(i^2) - E(i)^2, but I cannot get the same answer. Any help would be appreciated!
Moments of uniform distribution If the random variable X follows uniform distribution over range of values for x : (a, b), then its mean is (a+b)/2 and variance is (1/12)*(b-a)^2. You can refer to formulas and tables book to get these formulas. here, the random variable is annual rate of interest and it is uniformly distributed over range of values (2%, 6%). So, its mean is : (2% + 6%)/2 = 4% and variance is: (1/12)* (6% - 2%)^2 = given value in notes. You can derive the moments too from properties of uniform distribution. Formula you gave for variance is correct except that you may want to use (n-1) in the denominator if it were to be an unbiased estimator for population variance. (more of CT3 stuff...). Please let me know if this answers your question or have any more... Thanks, Raj
