ECO220Y1 Chapter Notes - Chapter 9: Probability Density Function, Probability Distribution, Normal Distribution
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ECO220Y1 Full Course Notes
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9. 8: continuous random variables: not all random variables can be modeled with discrete probability distributions, distribution of continuous random variable can be shown with a curve. Probability density function (pdf), denoted as f(x) Density function characteristics: non-negative for every possible value, total area under curve equals 1. Total probability bust be assigned somewhere under curve: probability x lies in interval a to b is equal to area under density function from a to b. Probability of any particular value is zero: probability that x lies in any interval depends only on length of interval. 9. 9 uniform distribution: all events equally likely. For values c and d (c (cid:3409) d) within [a, b] P(c (cid:3409) x (cid:3409) d) = (d - c) / (a - b) Mean is balancing point of curve: e(x) = a+b / 2, var(x) = (b-a)2 / 12. Normal probability plots: plot x against normal scores, distribution is normal if plot diagonal straight line, can identify outliers.
