Comparing the coefficients of the power of t on

both sides, we get

Variance (μ2) = npq, μ3 = npq(qp).

             μ4 = npq [1 + 3(n − 2)pq].

Therefore, Pearson's constants for binomial distributions are

 

images

 

Hence, for a binomial distribution,

Mean (μ) = np,

Variance (σ2) = npq,

Standard deviation (σ) = √npq,

Skewness images

Kurtosis images

We observe that

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

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