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5. Show the binomial distribution's probability mass function ,f(x) = () pª (1 – p)"-", sums to 1 over the support/domain x=0,1,2,...,n where 0

5. Show the binomial distribution's probability mass function ,f(x) = () pª (1 – p)"-", sums to 1 over the support/domain x=0,1,2,...,n where 0

MATLAB: An Introduction with Applications
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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**Problem 5:** Show that the binomial distribution’s probability mass function, \( f(x) = \binom{n}{x} p^x (1-p)^{n-x} \), sums to 1 over the support/domain \( x = 0, 1, 2, \ldots, n \), where \( 0 < p < 1 \) and \( n \) is a positive integer. **Hint:** Remember the binomial theorem.
Transcribed Image Text:**Problem 5:** Show that the binomial distribution’s probability mass function, \( f(x) = \binom{n}{x} p^x (1-p)^{n-x} \), sums to 1 over the support/domain \( x = 0, 1, 2, \ldots, n \), where \( 0 < p < 1 \) and \( n \) is a positive integer. **Hint:** Remember the binomial theorem.
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From the given information, the probability mass function of binomial random variable X is

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