Exercise5.1 Let Y1, ...,Yn be arandomsample. 1. Showthatthe j-th samplemoment mj = 1 n ni =1Y j

Exercise5.1 Let Y1, ...,Yn be arandomsample.

1. Showthatthe j-th samplemoment mj = 1 n Σni

=1Y j i is aconsistentestimatorofthe j-th moment

μj = EY j.

2. Assume that μ2 j < ∞. Showthat mj is aCANestimatorof μj with asymptoticvariance μ2 j−μ2j

.