Finding Mean and Standard Deviation for PDF Function
Refere to attachment for better formula representation. Let (Y1, Y2,...Yn) be a random sample from a uniform probabilitydensity functions (p.d.f) given by:
f (y;theta) = (1-theta)^-1, theta<y<1
f (y;theta) = (1-theta)^-1, theta<y<1
a. Find the mean of Y and shown that the variance of Y is (1-theta)^2/12
b. Show that theta = 2(sum Y/n) -1 is an unbiased estimator of theta.
c. Show that Var (theta0 = (1- theta)^2/3n
b. Show that theta = 2(sum Y/n) -1 is an unbiased estimator of theta.
c. Show that Var (theta0 = (1- theta)^2/3n
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