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intro-probability

# intro-probability - Primer on Probability for Discrete...

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Primer on Probability for Discrete Variables BMI/CS 576 www.biostat.wisc.edu/bmi576.html Mark Craven Fall 2011 Definition of probability frequentist interpretation: the probability of an event from a random experiment is the proportion of the time events of same kind will occur in the long run, when the experiment is repeated examples – the probability my flight to Chicago will be on time – the probability this ticket will win the lottery – the probability it will rain tomorrow always a number in the interval [0,1] 0 means “never occurs” 1 means “always occurs”

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Sample spaces sample space : a set of possible outcomes for some event examples – flight to Chicago: {on time, late} – lottery: {ticket 1 wins, ticket 2 wins,…,ticket n wins} – weather tomorrow: {rain, not rain} or {sun, rain, snow} or {sun, clouds, rain, snow, sleet} or… Random variables random variable : a variable representing the outcome of an experiment example X represents the outcome of my flight to Chicago – we write the probability of my flight being on time as P ( X = on-time) – or when it’s clear which variable we’re referring to, we may use the shorthand P (on-time)
Notation uppercase letters and capitalized words denote random variables lowercase letters and uncapitalized words denote values we’ll denote a particular value for a variable as follows we’ll also use the shorthand form for Boolean random variables, we’ll use the shorthand P ( Fever = true ) P ( X = x ) P ( x ) for P ( X = x ) P ( fever ) for P ( Fever = true ) P ( ¬ fever ) for P ( Fever = false ) Probability distributions if X is a random variable, the function given by P ( X = x ) for each x is the probability distribution of X requirements: P ( x ) = 1 x " 0.2 0.3 0.1 P ( x ) " 0 for every x

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intro-probability - Primer on Probability for Discrete...

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