# 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.

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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graulhavav9
Step 1
I guess you mean the cumulative distribution function F(k;n,p) of the (discrete) binomial distribution with number of trials $n\ge 0$ and success probability $0\le p\le 1.\phantom{\rule{thickmathspace}{0ex}}$.
Step 2
The probability mass functions (PMF) is
$f\left(k;n,p\right)=\left(\genfrac{}{}{0}{}{n}{k}\right){p}^{k}\left(1-p{\right)}^{n-k}$
and the CDF can be expressed with normalized incomplete Beta function
$F\left(k;n,p\right)=\sum _{i=0}^{k}f\left(k;n,p\right)={I}_{1-p}\left(n-k,k+1\right)$
###### Did you like this example?
ohgodamnitw0
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
$F\left(k\right)=\mathbb{P}\left(X\le k\right)$
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.