Calculating Variance

Probability · Axiom Academy

Computing variance and standard deviation of a discrete random variable A discrete random variable X has the following probability mass function: Excellent work! You've completed this variance calculation. Here's what we learned: Expected Value: E[X] = Σ x · P(X = x) gives the mean of the distribution. Variance Formula: Var(X) = E[X²] - (E[X])² is often easier to compute than the definition Var(X) = E[(X - μ)²]. Two Methods: Both formulas give the same result. The computational formula E[X²] - (E[X])² is typically more efficient. Standard Deviation: σ = √Var(X) gives the typical spread in the same units as X, making it more interpretable. Interpretation: A variance of 0.81 and standard deviation of 0.9 indicate moderate variability around the mean of 1.7. Understanding variance helps quantify the spread and uncertainty in random variables!

This is the written version of the interactive lesson above. See the full Probability course.