03 14 2013 Chapter 8 Random Variable Its value is based on the outcome of a random event Discrete Random Variable When we can list all outcomes Continuous Random Variable A random variable that can take on any value between 2 values For both DISCRETE and CONTINUOUS variables the collection of all possible values and the probabilities associated with them Expected Value Of a Discrete random variable is found by multiplying each possible value of the random variable by the probability that it occurs and then summing all those products Variance The expected value of those squared deviations The expected value of the sum or difference of random variables is the sum or difference of their expected values Addition Rule The variance of the sum or difference of two independent random variables is the sum of their individual variances The expected value of the sum of two random variables is the sum of the expected values The expected value of the difference of two random variables in the difference of the expected values If the random variables are independent the variance of their sum or difference is always the sum of the variances Probability Density Function PDF Must stay positive for every possible value and the total area under the curve must be exactly 1 0 Every Value of a continuous random variable has probability 0 Normal Models roughly symmetric Appropriate for distributions whose shapes are unimodal and The sum or difference of two independent Normal random variables is also Normal
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