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=√(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`