Question

Consider a random variable X that is normally distributed.If a random variable X is normally distributed, what will be the shape of the distribution of the sample mean?
(A) Normal
(B) Skewed left
(C) Skewed right
(D) Cannot be determined

Answer 1

Answer:

a. Normal

Step-by-step explanation:

Hello!

Let X₁, X₂, ..., Xₙ be random variables that constitute a random sample, then any function of type Ô = h that depends solely on the n random variables and does not contain any unknown parameters is called the estimator of parameter θ. When this function h (.) It is applied to the set of the n numerical values ​​of the respective random variables, a numerical statistic value is generated that receives the estimator name of the parameter Ô.

The function h (.) It is a function of random variables, so it is also a random variable, as a consequence of this, the estimator Ô has probability distribution with E (Ô) and V (Ô).

Applied to the normal distribution, if you have a random sample of n random variables X₁, X₂, ..., Xₙ that have a normal distribution, the sample mean calculated from this sample will be a random variable with the same distribution as the original variables.

X~N(μ;δ²) ⇒ X[bar]~N(μ;δ²/n)

I hope it helps!