Transcription of RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS
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RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS
RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS . 1. D ISCRETE RANDOM VARIABLES . Definition of a Discrete RANDOM Variable. A RANDOM variable X is said to be discrete if it can assume only a finite or countable infinite number of distinct values. A discrete RANDOM variable can be defined on both a countable or uncountable sample space. PROBABILITY for a discrete RANDOM variable. The PROBABILITY that X takes on the value x, P(X=x), is defined as the sum of the probabilities of all sample points in that are assigned the value x. We may denote P(X=x) by p(x).
Notice that the denominators of the five fractions are the same and the numerators of the five fractions are 1, 4, 6, 4, 1. The numbers in the numeratorsis a setof binomial coefficients. 1 16 = 4 0 4 16 = 4 1 6 16 = 4 2 4 16 = 4 3 1 16 = 4 4 We can then writethe probability massfunction as Date: August 20,2004. 1
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