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The Rayleigh density function is sometimes used by engineers to model lengths of life of electronic components and is given by: (²) e-y²/0 f(y)= y>0 elsewhere (a) Find E(Y). (b) If Y has the Rayleigh density, find the probability density function for U = Y² using the transformation method. Explain why the transformation method can be used for U-Y2 even though h(y) = y² is not monotonic over the entire real line. (Hint: do we need to account for P(Y y) for y ≤ 0?) (c) Find V(Y) using your answer in parts (a) and (b) (i.e. calculate E(U)).

The Rayleigh density function is sometimes used by engineers to model lengths of life of electronic components and is given by: (²) e-y²/0 f(y)= y>0 elsewhere (a) Find E(Y). (b) If Y has the Rayleigh density, find the probability density function for U = Y² using the transformation method. Explain why the transformation method can be used for U-Y2 even though h(y) = y² is not monotonic over the entire real line. (Hint: do we need to account for P(Y y) for y ≤ 0?) (c) Find V(Y) using your answer in parts (a) and (b) (i.e. calculate E(U)).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 93E
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The Rayleigh density function is sometimes used by engineers to model lengths of life of electronic components and is given by: f(y) = {$** (2) e-y²/0 y>0 elsewhere (a) Find E(Y). (b) If Y has the Rayleigh density, find the probability density function for U = Y² using the transformation method. Explain why the transformation method can be used for U - Y2 even though h(y) = y² is not monotonic over the entire real line. (Hint: do we need to account for P(Y <y) for y ≤ 0?) (c) Find V(Y) using your answer in parts (a) and (b) (i.e. calculate E(U)).
Transcribed Image Text:The Rayleigh density function is sometimes used by engineers to model lengths of life of electronic components and is given by: f(y) = {$** (2) e-y²/0 y>0 elsewhere (a) Find E(Y). (b) If Y has the Rayleigh density, find the probability density function for U = Y² using the transformation method. Explain why the transformation method can be used for U - Y2 even though h(y) = y² is not monotonic over the entire real line. (Hint: do we need to account for P(Y <y) for y ≤ 0?) (c) Find V(Y) using your answer in parts (a) and (b) (i.e. calculate E(U)).
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