Let X be a RV. The number of successes X in n independent Bernoulli trials with probability p of success. This is called a binomial RV with parameters (n,p) with pmf p(k)=(knā)pk(1āp)nāk,Ā kāX={0,1,āÆ,n}For RV Xā¼\mboxBinomial(n,p) āE[X]=np\mboxVar(X)=np(1āp)ā
The number of successes X in n independent Bernoulli trials with probability p