How do you find the mean and standard deviation of a binomial random variable?

Question

How do you find the mean and standard deviation of a binomial random variable?

 

What do these values tell us about the binomial experiment? 

Answer 1

mean=np

standard deviation=sqrt(n*p*(1-p))

Do you need proof of this? Please find it here http://www.math.ubc.ca/~feldman/m302/binomial.pdf it is hard to type it in here.

If we repeat binomial experiment many times mean is going to be around np within the region that is proportional to square root of number of experiments and the region is maximum the largest for p=0.5 because derivative of p*(1-p)=1-2p=0 when p=0.5 and second derivative is -2, so the function of p*(1-p) is concave down.