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PROBABILITY DISTRIBUTIONS (03/11/09) #6b A random variable is a numerical-valued function defined over a sample space which assigns a unique real number to each outcome of a probability experiment. A random variable may be discrete or continuous in nature. In other words, a value of a random variable is associated with the result of a chance or random event in a given probability experiment. Typically, the discrete random variable is a count of something . For example, if we toss 10 coins and observe the number of heads, then the number of heads observed may serve as the random variable x which can take on integer values from 0 to 10. Or, in an experiment of rolling two dice, we may define a random variable x to be the total number of dots showing; such a variable can take on integer values from 2 to 12. A probability distribution is a rule that associates each possible value of a random variable x with the probability P(x) of occurring of this value in a chance experiment . {It represents a theoretical population.} In other words, the probability distribution defines a function P(x) , that is called a probability distribution function , or simply a probability function . /* A function is a special type of relation that expresses how one quantity (the input ) depends on another quantity (the output ). If two variables x and y (which represent the input and output numbers respectively) are so related that to every value of one there corresponds exactly one value of the other, the second variable ( y ) is called a function of
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