Expected Value (Mean), Variance, and Standard Deviation (VCE SSCE Mathematical Methods): Flashcards

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Expected Value (Mean), Variance, and Standard Deviation
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Symbols for expected value of XX

μ\mu or E(X)E(X)

Formula for E(X)E(X) (discrete random variable)

E(X)=∑xx⋅p(x)E(X) = \sum_{x} x \cdot p(x)

Expected value represents which type of average?

Long-run average value over many trials

Property: E(aX+b)E(aX + b) equals

aE(X)+baE(X) + b

Does E(X2)=[E(X)]2E(X^2) = [E(X)]^2?

No, they are not equal in general

Formula for E[g(X)]E[g(X)]

∑xg(x)⋅p(x)\sum_{x} g(x) \cdot p(x)

Symbols for variance of XX

Var(X)\text{Var}(X) or σ2\sigma^2

Computational formula for Var(X)\text{Var}(X)

E(X2)−[E(X)]2E(X^2) - [E(X)]^2

Formula for standard deviation σ\sigma

Var(X)\sqrt{\text{Var}(X)}

Property: Var(aX+b)\text{Var}(aX + b) equals

a2Var(X)a^2\text{Var}(X)

Explore VCE SSCE Mathematical Methods Revision Notes by Topics

Discrete Random Variables

Sampling Without Replacement

Sampling with Replacement: The Binomial Distribution

Conditional Probability and Independence

Expected Value (Mean), Variance, and Standard Deviation

Explore VCE SSCE Mathematical Methods Model Answers by Topics

Discrete Random Variables

Sampling Without Replacement

Sampling with Replacement: The Binomial Distribution

Conditional Probability and Independence

Expected Value (Mean), Variance, and Standard Deviation

Explore VCE SSCE Mathematical Methods Quizzes by Topics

Discrete Random Variables

Sampling Without Replacement

Sampling with Replacement: The Binomial Distribution

Conditional Probability and Independence

Expected Value (Mean), Variance, and Standard Deviation

Explore VCE SSCE Mathematical Methods Exam Questions by Topics

Discrete Random Variables

Sampling Without Replacement

Sampling with Replacement: The Binomial Distribution

Conditional Probability and Independence

Expected Value (Mean), Variance, and Standard Deviation

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