Hello,

I have a few questions about statistics (mostly about estimators) that are more conceptual. I would greatly appreciate help!

the First is this:

1) Given that a variable x is normally distributed, what are thedistributions of the sample mean and sample variance of x?

2) How do you calculate the unbiased estimate of population mean? Given that we have the sample mean for a sample size of 49.

3) An economist has data on the employment status of n individuals. In particular, she has n observations X₁, X₂,..., X_n, where X_i= 1 if the individual is employed and X_i= 0 if the individual is unemployed. The economist would like to estimate the probability p that an individual isunemployed. a) Suggest an estimator for p. Briefly indicate why yours is a reasonable estimator of p. b) Find the bias, variance, and mean squared error of your estimator.