Expected Value and Variance

Statistics · Axiom Academy

LESSON Expected Value and Variance Review of expected value E(X) and variance Var(X) for random variables The expected value (or expectation) of a random variable X is the weighted average of all possible values, where weights are the probabilities. Sum over all possible values x i , multiplying each by its probability P(X = x i ) 2. Properties of Expected Value Expected value has several important properties that make it easy to work with: The variance measures how spread out the values of X are around the expected value. It's the expected squared deviation from the mean. Variance is the expected value of the squared distance from the mean Often easier to compute: "mean of squares minus square of mean" Variance behaves differently from expected value due to the squaring operation: Constants are squared when pulled out of variance! Adding a constant doesn't change the spread Only holds when X and Y are independent!

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