To find the variance of the bernoulli trial we use

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To find the variance of the Bernoulli trial, we use the formula E ( x ) = E ( x 2 ) { E ( x ) } 2 . For a single trial, there is E ( x 2 i ) = x i =0 , 1 f ( x i ) = p, V ( x i ) = p p 2 = p (1 p ) = pq, where q = 1 p . The outcome of the binomial random variable is the sum of a set of n independent and identical Bernoulli trials. Thus, the variance of the sum is the sum of the variances, and we have V ( x ) = n i =1 V ( x i ) = npq. 5
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  • Spring '12
  • D.S.G.Pollock
  • Variance, Probability theory, probability density function, variates

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