Calculating f(x) PDF Mean,Median,Mode & Plotting

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Homework Help Overview

The discussion revolves around determining constants for a probability density function (PDF) defined as f(x) = Ax - Bx^3 over the interval [0, 2]. The original poster seeks to establish a relationship between the mean and mode of the PDF, specifically that the mean is 0.9 times the mode, while also calculating the mean, median, and mode, and plotting the PDF.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the definitions of mean and mode in the context of a PDF and suggest setting up equations based on the relationship between mean and mode. There is mention of integrating the function to find the mean and questions about the correctness of the differentiation process to find the mode.

Discussion Status

The discussion includes attempts to derive equations for the constants A and B based on the properties of the PDF. Some participants express uncertainty about their calculations, while others provide supportive feedback, indicating a collaborative effort to clarify the problem without reaching a definitive conclusion.

Contextual Notes

There is an emphasis on ensuring the PDF integrates to 1 over its domain, which is a critical constraint in the discussion. The original poster mentions having the answers but struggles with the derivation process, indicating a potential gap in understanding the underlying concepts.

abhipatel
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Determine constants A and B such that function f(x) is a valid PDF whose mean is 0.9 times its mode.

f(x) = Ax- Bx ^3 , 0 <= x <= 2, otherwise = 0

Also calculate its mean,median and mode and plot the PDF

Please help...am scratching my head...have the answers but cannot derive the solution

Answers : A = 0.8466 ; B = 0.1733 ; Mean = 1.1485 , Median = 1.1724 , Mode = 1.2761
 
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What are the definitions of mean and mode for a PDF? Set mean=mode*0.9. That gives you one equation in A and B. Now remember a PDF needs to have integral=1 over it's domain. That gives you another equation for A and B. Solve them.
 
got one function...believe am screwing up in equating the mode and the mean i believe...mean is integral of x.f(x)dx right? basically integrate the function with limits 0 & 2...allright so u get 8A/3 - 32B/5 as Mean...Mode...am doing df(x)/dx...i don't know if that is correct?? thanks though am getting a good picture now...just a lil twist needed..
 
got it my friend...excellent help..thanks a lot buddy..take care
 

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