RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS

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RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS1. DISCRETE RANDOM of a Discrete RANDOM RANDOM variable X is said to bediscreteif it canassume only a finite or countable infinite number of distinct values. A discrete RANDOM variablecan be defined on both a countable or uncountable sample for a discrete RANDOM 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. Wemay denote P(X=x) by p(x). The expression p(x) is a function that assigns probabilities to eachpossible value x; thus it is often called the PROBABILITY function for distribution for a discrete RANDOM PROBABILITY distribution for adiscrete RANDOM variable X can be represented by a formula, a table, or a graph, which providesp(x) = P(X=x) for all x. The PROBABILITY distribution for a discrete RANDOM variable assigns nonzeroprobabilities to only a countable number of distinct x values. Any value x not explicitly assigned apositive PROBABILITY is understood to be such that P(X=x) = function f(x) p(x)= P(X=x) for each x within the range of X is called theprobability distributionof X.

RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS 1. DISCRETE RANDOM VARIABLES 1.1. 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. 1.2.

  Distribution, Variable, Probability, Random, Random variables and probability distributions, Random variables