Let X1, X2, X3, …, Xn sim N(mu, sigma^2) where mean mu and variance sigma^2 are unknown. Let S^2 = 1/nsum(Xi-overlineX)^2 and s^2 = 1/n-1sum(Xi-overlineX)^2. Which one of the following is correct according to the efficiency criterion?

(B) s^2 is less efficient than S^2.

Q3Section I (Objective (Q1–Q80))3 of 80

Statistical Inference — efficiency of the two sample variances

Let $X_1, X_2, X_3, …, X_n \sim N(\mu, \sigma^2)$ where mean $\mu$ and variance $\sigma^2$ are unknown. Let $S^2 = \frac{1}{n}\sum(X_i-\overline{X})^2$ and $s^2 = \frac{1}{n-1}\sum(X_i-\overline{X})^2$ . Which one of the following is correct according to the efficiency criterion?

Pick an option to check your answer. In a mock test a wrong answer here costs 0.83 mark.

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