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4 June, 00:12

Suppose we generate two uniform random numbers X and Y from [0, 1] independently. (1) What is the sample space?

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  1. 4 June, 00:25
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    A sample space is the set of all possible results of a random experiment.

    Let the random experiment be to choose a number in the interval [0, 1] and let X be the value chosen in that experiment.

    On the other hand, whether the random experiment is to choose a number in the interval [0, 1] and let Y be the value chosen in that experiment.

    Since the two experiments are independent, the sample space for the joint random variable (X, Y) is given by the cartesian product [0, 1] X [0, 1]
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