Answered: Suppose X follows an arbitrary…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Question

Suppose X follows an arbitrary distribution with mean μ and variance . We collected a sample and the sample size is 100. What is the distribution of the sample average and why can we make that claim? (Note: if you do not know how to insert the special characters like mu and sigma squared, just copy from the question)

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Expert Solution

Step 1

According to the Central Limit Theorem, when a sample of size $n$ is drawn from any population with mean $μ$ and variance $σ^{2}$ , the for large value of $n (\geq 30)$ , the sampling distribution of the sample mean is approximately normal with mean $μ$ and variance $\frac{σ^{2}}{n}$ .