1.3.6.6.18. Binomial Distribution
itl.nist.gov › div898 › handbookCumulative Distribution Function The formula for the binomial cumulative probability function is \( F(x;p,n) = \sum_{i=0}^{x}{\left( \begin{array}{c} n \\ i \end{array} \right) (p)^{i}(1 - p)^{(n-i)}} \) The following is the plot of the binomial cumulative distribution function with the same values of p as the pdf plots above.
Binomial distribution - Wikipedia
https://en.wikipedia.org/wiki/Binomial_distributionIf X ~ B(n, p), that is, X is a binomially distributed random variable, n being the total number of experiments and p the probability of each experiment yielding a successful result, then the expected value of X is: This follows from the linearity of the expected value along with the fact that X is the sum of n identical Bernoulli random variables, each with expected value p. In other words, if are identical (…
Tables of the Binomial Cumulative Distribution
www.uvm.edu › F21 › notesTables of the Binomial Cumulative Distribution The table below gives the probability of obtaining at most x successes in n independent trials, each of which has a probability p of success. That is, if X denotes the number of successes, the table shows 0 ()(1) x nrnr r r PXxCpp− = ≤=−∑