Find the cdf given a pdf with absolute value

[aquaelmo]

Homework Statement

Consider a continuous random variable X with the probability density function f_X(x) = ^|x|/₅ , – 1 ≤ x ≤ 3, zero elsewhere.
I need to find the cumulative distribution function of X, F_X (x).

2. Homework Equations
The equation to find the cdf.

The Attempt at a Solution

F_X(x) = ∫_-1^{x -u}/₅ du + ∫_-1^{0 -u}/₅ du + ∫₀^{x u}/₅ du

For some reason, my result is just a constant, but I can't figure out why my equation is wrong?

 

[LCKurtz]

Homework Statement

Consider a continuous random variable X with the probability density function f_X(x) = |x|/5 , – 1 ≤ x ≤ 3, zero elsewhere.
I need to find the cumulative distribution function of X, F_X (x).

2. Homework Equations
The equation to find the cdf.

The Attempt at a Solution

F_X(x) = ∫_-1^x -u/5 du + ∫_-1⁰ -u/5 du + ∫₀^x u/5 du

For some reason, my result is just a constant, but I can't figure out why my equation is wrong?

You have to do two cases. First take $-1\le x \le 0$ and work that. You will just need one integral. Then take $x>0$ and work that, which will take two integrals with $x$ only in the second one, etc.

 

[aquaelmo]

Oh I understand, the solution will have two cases. Thank you!

 

[LCKurtz]

I believe that's what I'm doing.
For case -1 ≤ x ≤ 0, I compute the integral ∫_-1^{x -u}/₅ du.
For the case x > 0, I compute the area of the first case, ∫_-1^{0 -u}/₅ du, then the second case, ∫₀^{x u}/₅ du

No, the second case would be $\int_{-1}^0 -\frac u 5~ du + \int_0^x \frac u 5 ~du$.