Let X∼Binomial(n,p)X \sim \text{Binomial}(n, p)X∼Binomial(n,p). Find the expected value of XXX given that X≥1X \ge 1X≥1.
np1−(1−p)n\frac{np}{1 - (1-p)^n}1−(1−p)nnp
npnpnp
np(1−p)1−(1−p)n\frac{np(1-p)}{1 - (1-p)^n}1−(1−p)nnp(1−p)
\frac{np}{1-p}