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3.3 Probability Distributions 31 3.3.2 Continuous Distributions: Rendezvous with Density 2 If you think carefully about a continuous outcome space, you realize that it becomes problematic to talk about the probability of a specific value on the continuum, as opposed to an interval on the continuum. For example, the probability that I eat exactly 2319.58372019. . . calories today is essentially nil, and that is true for any exact value you care to think of. We can, however, talk about the probability of intervals. The probability that I eat between 2000 and 2500 calories today is, say, 0.43. The problem with using intervals, however, is that their widths and edges are arbitrary, and very wide intervals are not precise. So what we will do is make the intervals infinitesimally narrow, and instead of talking about the infinitesimal probability of that infinitesimal interval, we will talk about the ratio of the probability to the interval width. That ratio is called the probability density. Examples and further explanation follow. Consider a spinner of the kind often found with board games. It has an arrow mounted on a hub in the center, and a flick of the finger makes the arrow spin around. Friction causes the arrow to stop eventually, pointing in a random