Question: A random variable Z is normally distributed with zero mean and unit variance. Show that E[/Z/] = sqrt(2pi)= (where / /denotes absolute value). A random

  1. A random variable Z is normally distributed with zero mean and unit variance. Show that E[/Z/] = sqrt(2pi)= (where / /denotes "absolute value").
  2. A random variable Y is normally distributed with zero mean and variance sigma^2 . Use the result in part (1) to show that sigma_hat =sqrt(2pi) */Y/ is an unbiased estimator of sigma.

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