Question

Exercise 1: A random sample from a size n has been selected from a statistical population having a mean and variance µ and $\sigma^2$ respectively. For sample mean $\bar{X}$ prove that $E(\bar{X}) = \mu$ $\sigma^2_{\bar{X}} = \frac{\sigma^2}{n}$. Exercise 2: a random sample from a size n has been selected from a normal population of a mean and variance µ and $\sigma^2$ respectively. For the sample mean $\bar{X}$ prove that $\bar{X} \sim N(\mu, \frac{\sigma^2}{n})$

          Exercise 1: A random sample from a size n has been selected from a statistical
population having a mean and variance µ and $\sigma^2$ respectively. For sample mean $\bar{X}$
prove that $E(\bar{X}) = \mu$ $\sigma^2_{\bar{X}} = \frac{\sigma^2}{n}$.
Exercise 2: a random sample from a size n has been selected from a normal population
of a mean and variance µ and $\sigma^2$ respectively. For the sample mean $\bar{X}$ prove that
$\bar{X} \sim N(\mu, \frac{\sigma^2}{n})$

Exercise 1: A random sample from a size n has been selected from a statistical
population having a mean and variance µ and σ^2 respectively. For sample mean X̅
prove that E(X̅) = μ σ^2X̅ = (σ^2)/(n).
Exercise 2: a random sample from a size n has been selected from a normal population
of a mean and variance µ and σ^2 respectively. For the sample mean X̅ prove that
X̅∼ N(μ, (σ^2)/(n))

Added by James C.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Sheryl Ezze

08/06/2023

Step 1

The population mean is u and the population variance is 22. Show more…

Show all steps

Thanks for your feedback!

Exercise 1: A random sample of size n has been selected from a statistical population with a mean Î¼ and variance Ïƒ^2. For the sample mean X, Exercise 2: A random sample of size n has been selected from a normal population with a mean Î¼ and variance Ïƒ^2. For the sample mean X, prove that X ~ N(Î¼, Ïƒ^2/n).