median of the probability density function shown

[gritty walrus]

If the PDF is $f(x)$ for $x>0$, and the median $m$ can be found in this way
$$\int_{0}^m f(x)=0.5$$

[steady cape]

! 拉夫

[pulsar glen]

how would I do it with the piecewise function?

[gritty walrus]

Have you find the equations yet?

[pulsar glen]

1/3x and -1/2x

[gritty walrus]

Alright so

Integral is nothing but

Area under the curve

Agreed?

[pulsar glen]

yes

[gritty walrus]

So

From 0 to 6, the area we have is

0.5 times 6 times 0.2

,calc 0.560.2

[steady cape]

Result:

0.6

[gritty walrus]

That's more than 0.5

Which means the median lies somewhere before 6

Does that make sense?

[pulsar glen]

ye

yes

oh i see now

so f(x) would just be 1/3x

[gritty walrus]

Which means that now we know which piece of the puecewise to integrate:)

[pulsar glen]

thanks a lot

[gritty walrus]

Actually sometimes

You may have to first integrate from 0 to 6

And then 6 to some other number m

To find the median

But in this case it was not needed

Does that make sense why?

[pulsar glen]

if the median is in the second half?

[gritty walrus]

Correct!

If you are lucky

And the visuals are correct

You can figure out where the median lies

By looking at the skewered graph

Thats more of a lucky thing tho

[pulsar glen]

ok thanks