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) or pX(x). The expression pX(x) is a function that assigns probabilitiesto each possible value x; thus it is often called the PROBABILITY function for the RANDOM variable distribution for a discrete RANDOM PROBABILITY distribution for adiscrete RANDOM variable X can be represented by a formula, a table, or a graph, which providespX(x) = P(X=x) for all x.

serve as the probability distribution for a discrete random variable X if and only if it s values, pX(x), satisfythe conditions: a: pX(x) ≥ 0 for each value within its domain b: P x pX(x)=1,where the summationextends over all the values within itsdomain 1.5. Examples of probability mass functions. 1.5.1. Example 1.

  Distribution, Value, Functions