Probability and Statistics Review

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Presentation transcript:

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)

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

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)

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)

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, …

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

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