# Calculator of Mean And Standard Deviation for a Probability Distribution

Instructions: You can use step-by-step calculator to get the mean $$(\mu)$$ and standard deviation $$(\sigma)$$ associated to a discrete probability distribution. Provide the outcomes of the random variable $$(X)$$, as well as the associated probabilities $$(p(X))$$, in the form below:

X values (comma or space separated) =
P(X) values (comma or space separated)
Name of the random variable (Optional)

#### Mean And Standard Deviation for a Probability Distribution

More about the Mean And Standard Deviation for a Probability Distribution so you can better understand the results provided by this calculator. For a discrete probability, the population mean $$\mu$$ is defined as follows:

$E(X) = \mu = \displaystyle \sum_{i=1}^n X_i p(X_i)$

On the other hand, the expected value of $$X^2$$ is computed as follows:

$E(X) = \mu = \displaystyle \sum_{i=1}^n X_i p(X_i)$

and then, the population variance is :

$\sigma^2 = E(X^2) - E(X)^2$

Finally, the standard deviation is obtained by taking the square root to the population variance:

$\sigma = \sqrt{E(X^2) - E(X)^2}$

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