Question

fxdx=1/2
f(x)= 1/72x [0,12]
find the median m

Answer 1

can you post the question?

Answer 2

Let x be the continuous random variable over [a,b] with probability density function f. Then the median of the x-values is that number m such that f(x)dx=1/2
f(x)=1/72x,[0,12]
find the median m

Answer 3

before f(x)dx it has that big S with m at the top and a at the bottom

Answer 4

suddenly the probability got hard hmmm

Answer 5

i know how to do it normally but not to find m

Answer 6

is it
\[f(x)=\frac{1}{72}x\]?

Answer 7

yes thats how f(x) looks

Answer 8

but im pretty sure you take the antiderivative of it

Answer 9

i guess you have to solve
\[\int_0^b\frac{xdx}{72}=\frac{1}{2}\] for \(b\)

Answer 10

anti derivative is easy enough, it is \(\frac{x^2}{144}\)

Answer 11

and since if you evaluate it as zero you got zero, you are left with solving
\[\frac{x^2}{144}=\frac{1}{2}\]

Answer 12

so x^2=72? @satellite73

Answer 13

where does m come into play?

Answer 14

that is all \[x=\sqrt{72}\]

Answer 15

thats the median?

Answer 16

yup

Answer 17

sweet thank you!

Answer 18

yw