(a) Explain how the sample raw moments provide consistent estimators for the distribution moments, but their finite sample properties invoke the existence of much higher moments that (i) are often difficult to justify and (ii) would introduce major imprecision in the resulting inference from their estimation.

(b) Compare the first few moments of the sample mean from a generic IID sample (no distributional assumption) with those of the sample variance.

(c) Explain how the sample mean, variance, standard deviation, third and fourth central moments as well as the skewness and kurtosis coefficient variances simplify substantially and are rendered considerably more precise when a distributional assumption such as Normality is invoked.