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When we are talkng about a binomial distribution

I can understand the meaning of np (that it is the mean), cause we assign a "absolute value", for what it is a "relative value", (the probability of succes, 0 to 1.00)

but when we are referring to the equation of variance

npq = variance.

Is there a way to interpret "pq", in the same way that we can interpet, "np"?

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    $\begingroup$ $q$ here must be $1-p$ $\endgroup$ Commented Jan 12, 2023 at 2:39
  • $\begingroup$ @kjetilbhalvorsen thank you for you answers, yes I know that q is 1-p, that it means the probability of failure but what I would like to know is the meaning of "pq" $\endgroup$
    – RodParedes
    Commented Jan 12, 2023 at 2:44
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    $\begingroup$ $pq$ means p multiplied by q $\endgroup$
    – Glen_b
    Commented Jan 12, 2023 at 5:34

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The sum of n Bernoulli(p) random variables is a binomial(n, p) random variable.

$p \cdot q = p \cdot (1-p)$ the variance of a Bernoulli random variable with a mean of p. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers is spread out from their average value. It is maximized when $p=q = \frac{1}{2}$, so failure and success are equally likely:

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  • $\begingroup$ Thank you @dimitriy !! $\endgroup$
    – RodParedes
    Commented Jan 15, 2023 at 13:09

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