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isdstest2 - ISDS Test 2 Study Guide 5.1 Random Variables A...

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ISDS Test 2 Study Guide 5.1 Random Variables A random variable is a numerical description of an experiment A random variable associates a numerical value with each possible experimental outcome The particular numerical value of the random variable depends on the outcome of the experiment A random variable can be classified as being either discrete or continuous depending on the numerical value it assumes Discrete Random Variables Discrete random variable – a random variable that may assume either a finite number of values or an infinite sequence of values such as 0, 1, 2, … X is a random variable because it provides a numerical description of the outcome of the experiment Continuous Random Variables Continuous random variable – a random variable that may assume any numerical value in an interval or collection of intervals Experimental outcomes based on measurement scales such as time, weight, distance, and temperature can be described by continuous random variables 5.2 Discrete Probability Distributions Probability distribution – for a random variable describes how probabilities are distributed over the values of the random variable Probability function – f(x); defines the probability distribution for a discrete random variable o The probability function provides the probability for each value of the random variable A primary advantage of defining a random variable and its probability distribution is that once the probability distribution is know, it is relatively easy to determine the probability of a variety of events that may be of interest to a decision maker Required Conditions For A Discrete Probability Function F(x) 1 Σ f(x) = 1 Can present probability distributions graphically o The values of the random variable x are shown on the horizontal axis and the probability associated with these values is shown on the vertical axis
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A formula that gives the probability function f(x) for every value of x is often used to describe probability distributions Discrete Uniform Probability Function F(x) = 1/n Where, n – the number of values the random variable may assume Evaluating f(x) for a given value of the random variable will provide the associated probability The more widely used discrete probability distributions generally are specified by formula Three important cases are the binomial, Poisson, and the hypergeometric distributions 5. 3 Expected Value and Variance Expected Value Expected value – aka mean, of a random variable is a measure of the central location for the random variable Expected Value of a Discrete Random Variable o E(x) = μ = Σ xf(x) This equation shows that to compute the expected value of a discrete random variable, we must multiply each value of the random variable by the corresponding probability f(x) and then add the resulting products Variance Use variance to summarize the variability in the values of a random variable
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isdstest2 - ISDS Test 2 Study Guide 5.1 Random Variables A...

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