**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:

#### 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:

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:

\[ \sigma = \sqrt{E(X^2) - E(X)^2}\]In case you have any suggestion, or if you would like to report a broken solver/calculator, please do not hesitate to **contact us**.