COMPSCI 70 Chapter Notes - Chapter 20: Exponential Decay, Exponential Distribution, Geometric Distribution
31 Jan 2018
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Document Summary
In a uniform distribution, the probability of choosing a number within an interval should only depend on the length of the interval. Geometric approach to calculating continuous uniform probabilities uniform distribution - is chosen uniformly randomly in the interval. To find the probability of an event involving two iid uniform random variables and , draw the unit square and shade in the region in the square which corresponds to the given event. The area of the shaded region is the desired probability. Because density of a uniform continuous distribution is constant and we know that integrals of all pdfs must be 1, , where is the pdf function and find that. The probability that is the area/region under the curve from the start of the interval to . The probability is simply a ratio of interval lengths. The expectation of a continuous uniform distribution is simply the midpoint of the two ends of the interval.
