Please state your assumptions and show all your work clearly.1. [40 marks] Show that the following equalities hold:a) Population variance:NNb) Sample variance:E,x)? n(x)?%3Dn – 1п — 1п — 1c) Sum of differences from the population mean:(xi - 4) = 0i=1

The variance of the data is used as a measure of spread, i.e. how munch is the data spread around…

Answered: a) Population variance: N N b) Sample…

a) Population variance: N N b) Sample variance: n(x)2 | п — 1 п — 1 n – 1 c) Sum of differences from the population mean: N 2(xi - 4) = 0 i=1

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

Please state your assumptions and show all your work clearly.
1. [40 marks] Show that the following equalities hold:
a) Population variance:
N
N
b) Sample variance:
E,x)? n(x)?
%3D
n – 1
п — 1
п — 1
c) Sum of differences from the population mean:
(xi - 4) = 0
i=1

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The mean is equal to of cellular phones of sold per day is therefore, it means that the average number To find the variance complete the table below: P(x) x2 - P(x) .2 X•P(x) 15 0.30 4.5 18 0.20 3.6 19 0.20 3.8 20 0.15 22 0.15 3.3 ix2 . P(x) = g? = ) [x² · P(x)] - u² = %3D %3D %3D while herefore, the variance of a probability distribution is equal to ne standard deviation is equal to such a igher ng