statistics

Variance of bernoulli distribution

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The_Don. answered · 16/04/2021

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Variance of Bernoulli Distribution

The expected value of Bernoulli Distribution is p

$V a r (x) = E [x^{2}] - [E {[x]]}^{2}$

$E [x] = p$

$E [x^{2}] = \sum_{x = 0}^{1} x^{2} P (x = x)$

$= 0^{2} \times p^{0} {(1 - p)}^{1 - 0} + 1^{2} \times p^{1} {(1 - p)}^{1 - 1}$

$= 0 + p$

$= p$

$V a r (x) = E [x^{2}] - [E {[x]]}^{2}$

$V a r (x) = p - {[p]}^{2}$

$= p [1 - p] = p q$

$= p q$

Thus the Variance of Bernoulli Distribution is given by; $p q$

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