Probabilities, Expected Values for Discrete Random VariablesX is called a “discrete” random variable if the possible values of X consist only of a finite or countable number of possible values. Generally, this means that X is a variable that is arrived at by counting something. In this case, X is said to have a “probability mass function” (often denoted pmf) of the form p(x). This is just a shorthand way of writing P[X=x}, where x is one of the possible values of the random variable X. A function p(x) is a pmf if it satisfies the two requirements below (think of probabilities) …..1.p(x) is always greater than or equal to zero (and it is non-zero only for the possible values of the random variable X)2.the total of the values of p(x) is oneexamples1. p(1) =.3, p(2) = .5, p(3) = .2
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