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LECTURE 2: STATISTICS REVIEW RANDOM VARIABLES X is a random variable if it takes different values according to some probability distribution. Types of Random Variables : Discrete Random Variable o Takes on a finite or countable infinite number of values o Example: outcome of a coin toss Continuous Random Variable o Takes on any value in a real interval o Each specific value has zero probability o Example: height of an individual at UCLA A probability distribution is best described by the corresponding probability density function and 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 p 2 1 x ,..., x , x , is defined as: = ) f(x j { p ..., 1, j for ) x Pr(X x X for 0 j j = = Example: Coin Toss
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. 5 1 Heads Tails 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.
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