> Hi, > > I am working on a section in my text book on unbiased estimators, and for > several of the problems I have to find the expected value of x squared. I > have the solutions manual for the text book, but I can't figure out how they > computed the expected value. For example, for a binomial distribution with > parameters n, p and q = 1-p, they have the expected value of x squared > equals npq+n^2*p^2. Can someone please explain how they get this? Another > example is for a poisson distribution with parameter L. They have the > expected value of x^2 as L + L^2. Do I have to use the formula for the > expected value of x^2 and compute the sum? This seems very difficult for > both of these distributions.
If the variance V(X) is known you can use that V(X) = E(X^2) - (E(X))^2 which gives E(X^2) = V(X) + (E(X))^2 and in the binomial case you get npq + (np)^2. But if you are trying to find E(X^2) to compute the variance you have to rely on good old math. /LWn . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
