1. ## Probability density function

How do you get f(x) for XS 26b 2. (1)?

2. Originally Posted by chengbin

How do you get f(x) for XS 26b 2. (1)?
Equation of line passing through (3, 0) and (6, k).

Equation of line passing through (6, k) and (9, 0).

3. What is the equation of the line through the points (0,3) and (6,k)?

And what is the equation of the line through the points (6,k) and (0,9)?

Beaten to the punch by Mr. F!

4. What is the equation of the line through the points (3,0) and (6,k)?

note that the point is (3,0 ) and not (0,3)

two point form

(y-y1) / (y2 - y1) =(x-x1) / (x2 - x1)

(y - 0) / (k-0) = (x-3) / (6-3)

simplify and solve for y

y = (k/3) [x-3]

formulae on analytical geometry -----straight lines

5. Maybe little off-the-track, but an very easy way is to just equate the area of tri-angle = 1

1/2 x base x height = 1/2 x 6 x k = 1 => k = 1/3

6. I have to set up an integral (talk about practice for calculus)

I feel stupid that I didn't see that I find the equation of the line for it.

7. Originally Posted by chengbin
I have to set up an integral (talk about practice for calculus)

I feel stupid that I didn't see that I find the equation of the line for it.
No you don't (ignore the given solution), the pdf is a triangle the area under the curve has to be 1 for it to be a pdf, the base is 6, the height k, so the area is 3k=1, so k=1/3.

The given solution has been done by a moron, this question is to test your understanding of pdf's not of algebra and calculus.

CB

8. Originally Posted by CaptainBlack
[snip]
The given solution has been done by a moron, this question is to test your understanding of pdf's not of algebra and calculus.

CB