Exercises. Show all necessary solutions.1. A research worker wishes to estimate the mean of a population using a sample large enough thatthe probability will be 0.95 that the sample mean will not differ from the population mean bymore than 25 percent of the standard deviation. How large a sample should he take?2. Let X1, X2 be a random sample from N(0, 1). What is the distribution of each of the following?а. (Х2 — X1)/V2b. (X1+ X2)²/(X2 – X1)²c. (X2 + X1)//(X1 – X2)²d. X{/X?3. Derive the variance of the F distribution.4. If X has an F distribution with m and n degrees of freedom, argue that 1/X has an F distributionwith n and m degrees of freedom.5. Derive the variance of the Student's t distribution.6. If X is t-distributed, show that X? is F-distributed.

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1. A research worker wishes to estimate the mean of a population using a sample large enough that the probability will be 0.95 that the sample mean will not differ from the population mean by more than 25 percent of the standard deviation. How large a sample should he take?

1. A research worker wishes to estimate the mean of a population using a sample large enough that the probability will be 0.95 that the sample mean will not differ from the population mean by more than 25 percent of the standard deviation. How large a sample should he take?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

Exercises. Show all necessary solutions.
1. A research worker wishes to estimate the mean of a population using a sample large enough that
the probability will be 0.95 that the sample mean will not differ from the population mean by
more than 25 percent of the standard deviation. How large a sample should he take?
2. Let X1, X2 be a random sample from N(0, 1). What is the distribution of each of the following?
а. (Х2 — X1)/V2
b. (X1+ X2)²/(X2 – X1)²
c. (X2 + X1)//(X1 – X2)²
d. X{/X?
3. Derive the variance of the F distribution.
4. If X has an F distribution with m and n degrees of freedom, argue that 1/X has an F distribution
with n and m degrees of freedom.
5. Derive the variance of the Student's t distribution.
6. If X is t-distributed, show that X? is F-distributed.

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