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Probability and Statistics Review

Probability and Statistics Review. Purpose: Review basics of probability and statistics Define some terminology Revisit some important distributions Discuss how to analyze and characterize different probability distributions Discuss applicability to performance evaluation (and CPSC 601.08).

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Probability and Statistics Review

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  1. Probability and Statistics Review • Purpose: • Review basics of probability and statistics • Define some terminology • Revisit some important distributions • Discuss how to analyze and characterize different probability distributions • Discuss applicability to performance evaluation (and CPSC 601.08)

  2. Some Terminology (1 of 2) • Experiment (e.g., coin flipping) • Sample space (e.g., S ={Heads, Tails}) • Could be discrete or continuous • Outcome (e.g., Heads) • Event: successful outcome occurs • Randomness: unpredictable outcomes • Independence: unaffected outcomes

  3. Some Terminology (2 of 2) • Random variable X • Probability distributions • Could be discrete or continuous • Probability density function (pdf) • f(x) = P(X = x) • Cumulative Distribution Function (CDF) • F(x) = P(X < x) • CDF is integral of pdf (continuous case)

  4. Axioms of Probability • Probabilities are non-negative • For any event A in the sample space S, P(A) > 0 • Probabilities are normalized • P(S) = 1 • Mutually exclusive events • If A and B are mutually exclusive events, then P(A or B) = P(A) + P(B)

  5. Describing Distributions (1 of 2) • There are several ways to summarize the key properties of a distribution: • Central tendency: mean, median, mode • Variability: variance, standard deviation, coefficient of variation (CoV), squared CoV • Moments: 1st moment, 2nd moment, … • Central moments: 1st central moment, … • Modality, index of dispersion, skewness, kurtosis, variance coefficient, …

  6. Describing Distributions (2 of 2) • The most common summary statistics are the mean and the variance: • Mean: expected value (expectation) • Variance: mean squared deviation from mean • Mean is equal to the first moment • Variance can be calculated from the first moment and the second moment • Variance is equal to 2nd central moment

  7. Some Common Distributions • Uniform Distribution • Binomial Distribution • Geometric Distribution • Poisson Distribution • Exponential Distribution • Erlang Distribution • Gaussian (Normal) Distribution

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