prob.part13.27_28 - 1.2 DISCRETE PROBABILITY DISTRIBUTIONS...

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1.2. DISCRETE PROBABILITY DISTRIBUTIONS 19 where each outcome i , for i = 1, . . . , 6, corresponds to the number of dots on the face which turns up. The event E = { 2 , 4 , 6 } corresponds to the statement that the result of the roll is an even number. The event E can also be described by saying that X is even. Unless there is reason to believe the die is loaded, the natural assumption is that every outcome is equally likely. Adopting this convention means that we assign a probability of 1/6 to each of the six outcomes, i.e., m ( i ) = 1 / 6, for 1 i 6. ± Distribution Functions We next describe the assignment of probabilities. The deFnitions are motivated by the example above, in which we assigned to each outcome of the sample space a nonnegative number such that the sum of the numbers assigned is equal to 1. Defnition 1.2 Let X be a random variable which denotes the value of the out- come of a certain experiment, and assume that this experiment has only Fnitely many possible outcomes. Let Ω be the sample space of the experiment (i.e., the
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This note was uploaded on 09/15/2009 for the course SCF scf taught by Professor Scf during the Spring '09 term at Indian Institute Of Management, Ahmedabad.

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prob.part13.27_28 - 1.2 DISCRETE PROBABILITY DISTRIBUTIONS...

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