statistics

Mean of bernoulli distribution

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The_Don. answered · 16/04/2021

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Answer

Mean of Bernoulli distribution

The moments of the Bernoulli Distribution are computed as follows;

$U_{r}^{I} = E [X^{r}]$

$= \sum_{x = 0}^{1} X^{r} p (x = x)$

Upon replacing the values of x with 0 and 1

$= 0 \times P (x = 0) + 1 \times P (x = 1)$

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

$= p$

Thus the mean of Bernoulli Distribution is given by p

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