The mean and variance, respectively, of a binomial distribution for $n$ independent trails with the probability of success as $p$, are

1. $\sqrt{np},np\left ( 1-2p \right )$
2. $\sqrt{np},\sqrt{np\left ( 1-p \right )}$
3. $np,np$
4. $np, np\left ( 1-p \right )$

Straight and simple

Binomial Distribution :

It is nothing but a distribution where “n” independent events are occurring with same probability of success, called p

and the prob of failure is (1-p)

Now Mean:

As it is a Discreet Random Variable

Mean = p+p+p+p+p+…...n times =np

variance = np(1-p)
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