Question

Suppose that Y1,....Yn are i.i.d random variables with a N (μγ, σ^2y) distribution. How would the probability density of Y change as the sample size n increases?

a. As the sample size increases, the variance of ȳ decreases. So, the distribution of ȳ becomes highly concentrated around μy.
b. As the sample size increases, the variance of ȳ decreases. So, the distribution of ȳ becomes less concentrated around μ μy.
c. As the sample size increases, the variance of ȳ increases. So, the distribution of ȳ becomes highly concentrated around μy.
d. As the sample size increases, the variance of ȳ increases. So, the distribution of ȳ becomes less concentrated around μy

Answer 1

Answer:

A

Step-by-step explanation:

As the sample size n increases, the sample mean (μy) becomes a more accurate estimate of the parametric mean, so the standard error of the mean becomes smaller. Therefore, the variance of y decreases and the distribution of y becomes highly concentrated around μy.