What is the pdf of the sample maximum?

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Homework Help Overview

The discussion revolves around finding the probability density function (pdf) of the sample maximum of independent random variables, specifically for four variables with a given pdf defined over the interval (0,1).

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to understand how to derive the pdf of the sample maximum and expresses difficulty in finding relevant information. Some participants suggest breaking the problem into smaller parts, such as first determining the pdf of the maximum of two variables. There is a question raised about the implications of the random variables having the same pdf and their independence.

Discussion Status

The discussion is ongoing, with participants exploring different approaches to the problem. Some guidance has been offered regarding starting with a simpler case, but there is no consensus on the overall solution yet.

Contextual Notes

The original poster indicates a lack of resources in their textbook regarding this topic, which may affect the depth of the discussion.

Quincy
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Homework Statement



Consider independent random variables X1, X2, X3, and X4 having pdf:

fx(x) = 2x over the interval (0,1)
Give the pdf of the sample maximum V = max{X1,X2,X3,X4}.


The Attempt at a Solution



I can't find ANYTHING about how to solve this in the book, please help!
 
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One way to start is to try to split the problem into smaller steps, try to solve this one first:

Give the pdf of the sample maximum V = max{X1,X2}

Hint: If X1 is given, what is the probability that X2 is smaller for that value?
 
Klockan3 said:
Hint: If X1 is given, what is the probability that X2 is smaller for that value?

don't both X1 and X2 have the same pdf?...
 
Quincy said:
don't both X1 and X2 have the same pdf?...
Yes, and? Having the same pdf doesn't mean that they will always take the same value which is why they are called "independent random variables".
 

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