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

[abhipatel]

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

 

[Dick]

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.

 

[abhipatel]

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..

 

[abhipatel]

got it my friend...excellent help..thanks a lot buddy..take care