Find the cdf given a pdf with absolute value

  • #1
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Homework Statement


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

2. Homework Equations

The equation to find the cdf.

The Attempt at a Solution


FX(x) = ∫-1x -u/5 du + ∫-10 -u/5 du + ∫0x u/5 du

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

  • #2
LCKurtz
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Homework Statement


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

2. Homework Equations

The equation to find the cdf.

The Attempt at a Solution


FX(x) = ∫-1x -u/5 du + ∫-10 -u/5 du + ∫0x 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.
 
  • #3
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Oh I understand, the solution will have two cases. Thank you!
 
  • #4
LCKurtz
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I believe that's what I'm doing.
For case -1 ≤ x ≤ 0, I compute the integral ∫-1x -u/5 du.
For the case x > 0, I compute the area of the first case, ∫-10 -u/5 du, then the second case, ∫0x u/5 du
No, the second case would be ##\int_{-1}^0 -\frac u 5~ du + \int_0^x \frac u 5 ~du##.
 

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