Question

The mean of a binomial distribution is found using which of the following formulas?

p*q

q*x

n*p

p*x

Answer 1

solution:

Let X is Binomial random variable with n trials and for each trial probability of succes is p

X~B(n,p)

P(X=x) = nCx * (p)^x * (1-p)^n-x

The Expected value of X = Mean of X

= E[X]

  

since for X=0 ,the whole term is 0.

Let Y = x-1 and m = n-1

If X =1 then Y = 0

If X=n then Y = n-1

Then ,   

     

= np

Mean of Binomial distribution = n*p

Hence, Option-C is correct