What are the mean and standard deviation of a binomial probability distribution with #n=2 # and #p=4/17 #?

1 Answer
Jul 18, 2016

The mean is #mu=n*p=2* 4/17=8/17 approx 0.4706# and the standard deviation is #sigma=sqrt{n*p*(1-p)}=sqrt{2*4/17*13/17}=sqrt{104/289} approx 0.5999#

Explanation:

The special formulas #mu=n*p# and #sigma=sqrt{n*p*(1-p)}# only work for binomial random variables, where #n# is the number of independent trials with outcomes "success" or "failure", and #p# is the probability of "success" on each trial. The random variable #X# itself counts the number of successes in #n# trials.