GATE Mechanical 2021 Set 2 | Question: 3

Question

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

• A. $\sqrt{np},np\left ( 1-2p \right )$
• B. $\sqrt{np},\sqrt{np\left ( 1-p \right )}$
• C. $np,np$
• D. $np, np\left ( 1-p \right )$

Answer 1

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)