Problem with Statistics/probability/calculus?

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Homework Help Overview

The discussion revolves around a problem in statistics and probability, specifically focusing on a probability density function (pdf) related to vibratory stress on a wind turbine. The original poster seeks to prove that the given function is a valid pdf and to calculate probabilities based on a specific parameter value.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to demonstrate that the function is a pdf by showing it is greater than zero and considering the integral. Some participants suggest a substitution method for integration, while others clarify the role of the parameter y in the context of the problem.

Discussion Status

The discussion is ongoing, with participants exploring different approaches to integration and clarifying the nature of the parameter y. There is no explicit consensus on the method to proceed with the integration, but guidance has been offered regarding substitution.

Contextual Notes

Participants are navigating the complexities of integrating the pdf and confirming the status of y as a constant parameter in the problem setup.

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Homework Statement



let X denote the vibratory stress (psi) on a wind turbine at a certain wind speed. the pdf is

f(x;y) = (x/y^2)*(e^((-x^2)/(2y^2))

a) i need to prove that it is a pdf.
b)assume y=100, what is the probability X is at most/least 200? what's prob X les than 200

Homework Equations





The Attempt at a Solution




so i did part a part 1...f(x;y) is greter than 0 for all values...
but for the integral of f(x)=1, i think i need to know how to integrate that, and i have no idea how!
 
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Try the substitution u=x^2/(2*y^2).
 
y is a constant tho?
 
I think y is constant.
 
roadrunner said:
y is a constant tho?

Sure. You said you were integrating dx, right? y is just a parameter.
 

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