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Example 5-27. A gun is aimed at a certain point (origin of the coordinate system). Because of the random factors, the actual hit point can be any point (X,Y) in à circle of radius R about thè origin. Assume that the joint density of X and Y is constant in this circle given by : fr (x,y) = k, for *+ y's R? = 0, otherwise (i) Compute k, (i) show that %3D 1/2 2 fz ( x ) = TR- for -RSISR R = 0, otherwise

Example 5-27. A gun is aimed at a certain point (origin of the coordinate system). Because of the random factors, the actual hit point can be any point (X,Y) in à circle of radius R about thè origin. Assume that the joint density of X and Y is constant in this circle given by : fr (x,y) = k, for *+ y's R? = 0, otherwise (i) Compute k, (i) show that %3D 1/2 2 fz ( x ) = TR- for -RSISR R = 0, otherwise

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Example 5-27. A gun is aimed at a certain point (origin of the coordinate system). Because of the random factors, the actual hit point can be any point (X,Y) in à circle of radius R about thè origin. Assume that the joint density of X and Y is constant in this circle given by : fxr (x,y) = k, for x+ y's R? = 0, otherwise (i) Compute k, (ii) show that %3D %3D 2 1/2 2 fr (x)= R { for -RSISR - TR. R = 0, otherwise %3D
Transcribed Image Text:Example 5-27. A gun is aimed at a certain point (origin of the coordinate system). Because of the random factors, the actual hit point can be any point (X,Y) in à circle of radius R about thè origin. Assume that the joint density of X and Y is constant in this circle given by : fxr (x,y) = k, for x+ y's R? = 0, otherwise (i) Compute k, (ii) show that %3D %3D 2 1/2 2 fr (x)= R { for -RSISR - TR. R = 0, otherwise %3D
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