Comparing the coefficients of the power of t on
both sides, we get
Variance (μ2) = npq, μ3 = npq(q − p).
μ4 = npq [1 + 3(n − 2)pq].
Therefore, Pearson's constants for binomial distributions are
Hence, for a binomial distribution,
Mean (μ) = np,
Variance (σ2) = npq,
Standard deviation (σ) = √npq,
We observe that
- skewness of the binomial distribution is 0 for p = ,
- skewness is positive for p < ,
- skewness is ...