From the course: Probability Foundations for Data Science

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Discrete vs. continuous dispersion

Discrete vs. continuous dispersion

From the course: Probability Foundations for Data Science

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Discrete vs. continuous dispersion

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- Let's explore how to calculate variance and standard deviation for both discrete and continuous random variables. Let's begin with discrete random variables in understanding how variance and standard deviation are calculated for them. Let's look at X, which is a discrete random variable with possible values, X1 to Xn, and associated probabilities, P1 to Pn. Variance is calculated by this equation where you are summing from 1 to N with the value Xi subtracted by the expectation of X, and this whole thing is squared. And then, you multiply it by the associated probability, Pi. Remember, you calculate discrete expectation with this equation where you are summing from values 1 to N for each value Xi multiplied by its associated probability Pi. The standard deviation is simply the square root of the variance. So, sigma is going to represent standard deviation and that's equal to the square root of Rx. Or again, sometimes you'll see it as sigma squared. Let's look at this in an example…

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