STAT 3450 Lecture Notes - Lecture 6: Probability Distribution, Random Variable, Cumulative Distribution Function
6 Mar 2017
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Recall: a random variable x is continuous if the number of possible values is uncountable, contains an interval. A continuous random variable is a model for a quantity that in principal takes values of an interval, while in reality every measurement scale is discrete. Example: let t = time (minutes) it takes to complete an exam. The above curve is the probability density function of the continuous random variable t. The summation in discrete case is replaced by integration in the continuous case. Definition: a function fx : r [0, ) is the probability density function (pdf) of a continuous random variable x if for any a b, Xap b b a xf dx bxp bxp. Because cxp cp x c c c xf dx. Example: a container is designed to hold 12 fluid ounces. Due to variability in manufacturing, the exact number of fluid ounces that a container actually holds is between 11. 75 and 12. 25.
