(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

2. Relevant equations

The median of a function is

integral from m to infinity of f(x)dx = 1/2

3. 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.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Median of a Density Function

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