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

Question

Mathematics

Cortez Arellano

3 March, 02:42

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

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Answers (1)

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Karson Burch · Answer 1

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.