ECON10005 Lecture Notes - Lecture 10: Uncountable Set, Cumulative Distribution Function, Kurtosis
27 Jul 2018
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Document Summary
Set is infinite but shares the same size as the natural numbers. Can take any possible value along some continuum. Probability mass of a single value will be infinitely small. Defined on the interval [a,b] hence, probability mass associated with that interval must be 1. Mass must be distributed equally along the interval. 1 = (b-a) x h h = 1/(b-a) Height represents a probability density and allows us to compute the probability of intervals as opposed to individual points. Calculate the area underneath the density function to find probabilities. Probability density function is the slope of the cumulative distribution function. To derive the cumulative destribution we compute the anti-derivative of the uniform. Note: pdf is the derivative of the cdf. X is continues rv with density function fx, then. If fx is the corresponding cumulative distribution function, then. Probability that x will take some value in the interval [j,k] is given by.
