If N variables are normally distributed with the same mean and standard deviation, the true variance in the means among the N variables is zero. However, if the mean of each N_i is estimated from n samples, the estimated variance in the means among the N variables will be non-zero. What will the estimated variance be?
Thanks for your answers.
Originally Posted by ecotheory
Thanks captain, but could you either generalize to more than one N_i, or offer a hint of explanation for your answer so that I might? I guess I should have specified that the true variance of each N_i is also estimated from the samples.