What is the Median of a Density Function and How Can I Solve for It?

[ACE_99]

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.

 

[statdad]

The integral looks okay. In the equation try setting

$$u = m^2 \Rightarrow u^2 = m^4$$

Then solve the quadratic for $$u$$, and find $$m$$ from that. Remember that $$m$$ has to be between 0 and 3.

 

[ACE_99]

Thanks a lot, I tried that out and it works