06a Lesson 6 SM - x V X x f x dx - = =- (Property 8)...

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The 9 Properties of Continuous Distributions Verify that a function f(x) is a legitimate probability density function (PDF). 0 ) ( x f for all x (Property 1) 1 ) ( = - dx x f (Property 2) Understand that the probability assigned to any particular value of a continuous random variable is zero. 0 ) ( = = c X P (Property 3) Create a cumulative distribution function (CDF) using a continuous random variable's PDF. dy y f x X P x F x - = = ) ( ) ( ) ( (Property 4) Calculate probabilities associated with continuous random variables using either the PDF or the CDF. dx x f b X a P b a = ) ( ) ( (Property 5) ) ( ) ( ) ( a F b F b X a P - = (Property 6) Calculate the Expected Value and Variance of a continuous random variable. dx x f x X E x - = = ) ( * ) ( μ (Property 7) 2 2 ( ) ( ) * ( ) x
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Unformatted text preview: x V X x f x dx - = =- (Property 8) Understand how to find the (100 p )th percentile of a continuous random variable: Set ) ( * x F p = , solve for x* (Property 9) For example, if x e x F --= 1 ) ( , then solving for the inverse would yield: Now, you can find any percentile in the distribution. There are many ways to solve equations like this in Mathematica. Two of these methods are the Solve command and the FindRoot command. You must remember that you are simply using Mathematica as a tool. Therefore, it is up to you to determine which of these is suitable for you to find percentiles....
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06a Lesson 6 SM - x V X x f x dx - = =- (Property 8)...

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