Analyzing the Bias of Estimators for Variance

For access to Colab notebook in video, go to https://colab.research.google.com/dri... 0:00 - Why does the sample standard deviation, s, typically use n-1? 1:06 - Consider two different estimates for the population variance 3:04 - Stating the result we want to prove in Question 4a 4:34 - Proving Theorem 15.1 9:55 - Using Theorem 15.1 to prove statement in Question 4a 14:45 - Question 4b - Show s^2 is an unbiased estimate for the population variance 17:00 - Question 4c - Show sigma-hat^2 is a biased estimate for the population variance 19:00 - Summarizing our results about estimates for population variance 19:40 - Finally, here's why we often divide by n-1 with the sample standard deviation!