Question

Let 3 random samples of size n1=20, n2=10 & n3=8 be taken from a population with mean μ & variance σ2. Les S12, S22, & S32 be the sample variances. Show that S2 is an unbiased estimator of σ2.

Answer 1

\[S _{1}=(20S_{1}^2+10S_{2}^2+8S_{3}^2)/38\]