What is Cumulative Binomial probabilities? I am new to this so don't know if I am asking the right question as I just read about its usage but didn't know what exactly a Cumulative Binomial probability is.

rancuri5a 2022-10-02 Answered
What is Cumulative Binomial probabilities?
I am new to this so don't know if I am asking the right question as I just read about its usage but didn't know what exactly a Cumulative Binomial probability is.
So my question is, What is Cumulative Binomial probabilities ? any example will be of great help.
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Answers (2)

graulhavav9
Answered 2022-10-03 Author has 14 answers
Step 1
I guess you mean the cumulative distribution function F(k;n,p) of the (discrete) binomial distribution with number of trials n 0 and success probability 0 p 1. .
Step 2
The probability mass functions (PMF) is
f ( k ; n , p ) = ( n k ) p k ( 1 p ) n k
and the CDF can be expressed with normalized incomplete Beta function
F ( k ; n , p ) = i = 0 k f ( k ; n , p ) = I 1 p ( n k , k + 1 )
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ohgodamnitw0
Answered 2022-10-04 Author has 2 answers
Step 1
I sense that you are implicitly asking what a cumulative density function is. I apologize if this is not the case, and you can ignore what follows.
Imagine that your Binomial random variable represents the number of heads you obtain while flipping some coin n times (let's formally call this random variable X). Then, the cumulative density function (or CDF) is a function that tells you, for each natural number k, what is the probability that you will obtain at maximum k heads. If your coin is biased and it has a probability of showing heads equal p, the definition the CDF is
F ( k ) = P ( X k )
Step 2
This definition is general, it works for all random variables and not only Binomials! For the specific Binomial case, gammatester gave you the correct formula.
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