Example 387 given an angle expressed in radians let

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Unformatted text preview: tion of another. Suppose Y = g (X ) for some function g and a random variable X with a known pdf, and suppose we want to describe the distribution of Y. A general way to approach this problem is the following three step procedure: Step 1: Scope the problem. Identify the support of X. Sketch the pdf of X and sketch g. Identify the support of Y. Determine whether Y is a continuous-type or discrete-type random variable. Then take a breath–you’ve done very important ground work here. Step 2: Find the CDF of Y. Use the definition of the CDF: For any constant c, FY (c) = P {Y ≤ c} = P {g (X ) ≤ c}. In order to find the probability of the event {g (X ) ≤ c}, try to describe it in a way that involves X in a simple way. In Step 2 most of the work is usually in finding FY (c) for values of c that are in the support of Y. Step 3: Differentiate FY to find its derivative, which is fY . Typically the pdf gives a more intuitive idea about the distribution of Y than the CDF. 3.8. FUNCTIONS OF A RAND...
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This note was uploaded on 02/09/2014 for the course ISYE 2027 taught by Professor Zahrn during the Spring '08 term at Georgia Institute of Technology.

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