Engineering Mathematics, Volume II, Second Edition

 

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,

Skewness

Kurtosis

We observe that

1. skewness of the binomial distribution is 0 for p = ,
2. skewness is positive for p < ,
3. skewness is ...