Question

If X is a binomial random variable, compute the mean, the standard deviation, and the variance for each of the following cases:

(a) n=3,p=0.6
(b) n=6,p=0.7
(c) n=3,p=0.1
(d) n=4,p=0.7

Answer 1

If $X\sim\mathcal B(n,p)$, that is, $X$ is a random variable following a binomial distribution across $n$ trials and success probability $p$, then the mean, variance, and standard deviation of the distribution are $\mu=np$, $\sigma^2=np(1-p)$, and $\sigma=\sqrt{np(1-p)}$, respectively.

(a) $\mu=1.8,\sigma^2=0.72,\sigma\approx0.8485$

(b) $\mu=4.2,\sigma^2=1.26,\sigma\approx1.1225$

(c) $\mu=0.3,\sigma^2=0.27,\sigma\approx0.5196$

(d) $\mu=2.8,\sigma^2=0.84,\sigma\approx0.9165$