# What are the mean and standard deviation of a binomial

osnomu3 2022-01-17 Answered
What are the mean and standard deviation of a binomial probability distribution with n=2 and $p=\frac{4}{17}$?
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## Expert Answer

veiga34
Answered 2022-01-17 Author has 32 answers
The mean is $\mu =n\cdot p=2\cdot \frac{4}{17}=\frac{8}{17}\approx 0.4706$ and the standard deviation is
$\sigma =\sqrt{n\cdot p\cdot \left(1-p\right)}=\sqrt{2\cdot \frac{4}{17}\cdot \frac{13}{17}}=\sqrt{\frac{104}{289}}\approx 0.5999$
Explanation:
The special formulas $\mu =n\cdot p$ and $\sigma =\sqrt{n\cdot p\cdot \left(1-p\right)}$ 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.
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