Question

Suppose that are Yi.....Yn are i.i.d random variables with a Nâ(âμY, Ï^2Y â) distribution. How would the probability density of ȳ change as the sample size n âincreases? â
a. As the sample sizeâ increases, the variance of decreases.â So, the distribution of becomes less concentrated around.
b. As the sample sizeâ increases, the variance of decreases.â So, the distribution of becomes highly concentrated around.
c. As the sample sizeâ increases, the variance of increases.â So, the distribution of becomes highly concentrated around.
d. As the sample sizeâ increases, the variance of increases.â So, the distribution of becomes less concentrated around.

Answer 1

Answer:

b. As the sample size â increases, the variance of decreases. â So, the distribution of becomes highly concentrated around.

Step-by-step explanation:

Let : Yi,.... Yn are = i.i.d are random variables. The probability density of the distribution varies along with the sample size. When the sample size changes, the probability density of $E^3$ also changes.

The probability distribution may be defined as the statistical expression which defines the likelihood of any outcome for the discrete random variable and it can be opposed to the continuous random variable.

In the context, when the size of the sample of the distribution size increases, it causes a decrease in the variance and so the distribution becomes highly concentrated around.