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LECTURE 2: STATISTICS REVIEW RANDOM VARIABLES X is a random variableif it takes different values according to some probability distribution. Types of Random Variables: •Discrete Random Variable oTakes on a finite or countable infinite number of values oExample: outcome of a coin toss •Continuous Random VariableoTakes on any value in a real interval oEach specific value has zero probability oExample: height of an individual at UCLA A probability distribution is best described by the corresponding probability density functionand the cumulative distribution function.PROBABILITY DISTRIBUTION FUNCTION (PDF) A Probability Distribution Function summarizes the information concerning the possible outcomes of X and the corresponding probabilities. •The PDF of a discrete random variable X that takes on values, say p21x,...,x,x, is defined as: =)f(xj{p...,1,jfor )xPr(XxXfor 0jj==≠Example: Coin Toss
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. 51HeadsTails•The PDF of a continuous random variable is similar to that of a discrete random variable except we now measure the probability the random variable is in a certain range or interval. It is defined as the derivative of the cumulative distribution function (CDF) and is shown in the following graph.