prob.part24.49_50 - Chapter 2 Continuous Probability...

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Chapter 2 Continuous Probability Densities 2.1 Simulation of Continuous Probabilities In this section we shall show how we can use computer simulations for experiments that have a whole continuum of possible outcomes. Probabilities Example 2.1 We begin by constructing a spinner, which consists of a circle of unit circumference and a pointer as shown in Figure 2.1. We pick a point on the circle and label it 0, and then label every other point on the circle with the distance, say x , from 0 to that point, measured counterclockwise. The experiment consists of spinning the pointer and recording the label of the point at the tip of the pointer. We let the random variable X denote the value of this outcome. The sample space is clearly the interval [0 , 1). We would like to construct a probability model in which each outcome is equally likely to occur. If we proceed as we did in Chapter 1 for experiments with a finite number of possible outcomes, then we must assign the probability 0 to each outcome, since
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