11 ft t 1 e 22 the corresponding pdf is given by t2 ft

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Unformatted text preview: of in terms of percentiles. Consider, for example, the heights of all the people within a large group. Ignore ties. A particular person from the group is considered to be in the 90th percentile according to height, if the fraction of people in the group shorter than that person is 90%. So 90% of the people are in the 90th percentile or smaller. Similarly, 50% of the people are in the 50th percentile or smaller. So the percentile ranking of a randomly selected person from the group is uniformly distributed over the range from zero to one hundred percent. This result does not depend on the distribution of heights within the group. For this example, Y can be interpreted as the rank of X (expressed as a fraction rather than as a percentile) relative to the distribution assumed for X. 3.8. FUNCTIONS OF A RANDOM VARIABLE 3.8.2 109 Generating a random variable with a specified distribution An important step in many computer simulations of random systems is to generate a random variable with a specified CDF. This is often...
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