Show the binomial distribution's probability mass function ,f(x) =C) * (1 – p)"-a,sums to 1 over the support/domain x=0,1,2,...,n where 0 < p < 1 and n is a positive integer.

Answered: Show the binomial distribution's…

Show the binomial distribution's probability mass function ,f(x) = p* (1 – p)"-ª, sums to 1 over the support/domain x=0,1,2,...,n where 0 < p < 1 and n is a positive integer.

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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Question

Show the binomial distribution's probability mass function ,f(x) =
C) * (1 – p)"-a,
sums to 1 over the support/domain x=0,1,2,...,n where 0 < p < 1 and n is a positive integer.

Expert Solution

Step 1

The Probability mass function of binomial distribution is:-

$f_{X} (x) = \{\begin{cases} (\begin{matrix} n \\ x \end{matrix}) p^{x} {(1 - p)}^{n - x}, i f x = 0, 1, 2, 3, . . ., n \\ 0, o t h e r w i s e \end{cases}$

we have to show that the above probability mass function sums to 1 over the domain x=0,1,2,3,...,n where 0<p<1

To show this we just perform summation and use binomial theorem.

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