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ACE_99
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Homework Statement
The probability density function is defined as
f(x) = (4/81)x(9-x^2) for 0 <= x <= 3
= 0 for every other value
Find the median value of the density.
Homework Equations
The median of a function is
integral from m to infinity of f(x)dx = 1/2
The Attempt at a Solution
I took the integral from m to 3 of (4/81)x(9-x^2).
This turned out to be
(18/81)x^2 -(1/81) x^4 = 1/2
I then evaluated the left hand side from m to 3 and simplified so that only the variable m is left. The equation I got was
(1/81)m^4 - (18/81)m^2 = -1/2
I know that I am suppose to solve for m in order to get the median but I'm not sure how to do this, and I am also unsure whether my procedure is correct.
Any help would be great thanks. Sorry bout the formatting I'm new to this.