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An alternative proof of Theorem 2 may be based on the fact that if X1, X2, ..., and Xn are independent random variables having the same Bernoulli distribution with the parameter θ, then Y = X1 + X2 +···+ Xn is a random variable having the binomial distribution with the parameters n and θ. Verify directly (that is, without making use of the fact that the Bernoulli distribution is a special case of the binomial distribution) that the mean and the variance of the Bernoulli distribution are μ = θ and σ2 = θ (1 - θ ).
Theorem 2
The mean and the variance of the binomial distribution are
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Since the introduction in the UK of the Equal Pay Act in 1970, there has been considerable interest in monitoring the difference between women and men's pay. Official statistics, via the Office of National Statistics (ONS), play an important role ..
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