Suppose that Y1 Yn are i 1 d random variables with a Nueyi

Suppose that Y1 . Yn are i 1 d. random variables with a Nueyi distribution. How would the probability density of Y change as the sample size n increases? Hint: Think about the law of large numbers O A. As the sample size increases, the variance of Y increases. So, the distribution of Y becomes less concentrated around Y. O B. As the sample size increases, the variance of Y decreases. So, the distribution of Y becomes less concentrated around Y. O c. As the sample size increases, the variance o Y increases. So, the distribution of Y becomes highly concentrated around ( D. As the sample size increases, the variance of Y decreases. So, the distribution of Y becomes highly concentrated around

Solution

Correct option is (D).

As sample size becomes larger, the standard deviation decreases, therefore variance decreases. As a result, the distribution of the dependent variable (Y) becomes more concentrated around the mean.