Variance for Continuous RVs

Probability · Axiom Academy

LESSON Variance for Continuous RVs Measuring spread and dispersion around the mean The variance of a continuous random variable X measures the expected squared deviation from the mean: This is the average value of (X - E[X])², weighted by the probability density. Variance quantifies how far values typically fall from the expected value. The variance has an equivalent computational formula that is often easier to use: This "shortcut" formula says: variance equals the expected value of X² minus the square of the expected value. This form avoids having to compute (x - μ)² inside the integral. The standard deviation is the square root of the variance: Why use standard deviation? It has the same units as the original variable X, making it more interpretable. If X is measured in meters, variance has units meters², but standard deviation has units meters.

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