Transcription of RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS
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RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS
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)
4 RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS F(x)= 0 for x <0 1 16 for0 ≤ x<1 5 16 for1 ≤ x<2 11 16 for2 ≤ x<3 15 16 for3 ≤ x<4 1 for x≥ 4 1.6.4. Second example of a cumulative distribution function. Consider a group of N individuals, M of
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