Ok, this one's got me stumped!(adsbygoogle = window.adsbygoogle || []).push({});

Let's take as an example the probability density function for a random variable X so that:

f(x) = [itex]\frac{4}{3x^{3}}[/itex] 1≤x<2

f(x) = [itex]\frac{x}{12}[/itex] 2≤x≤4

f(x) = 0

So the CDF for this variable comes out as:

F(x) = [itex]\frac{-2}{3x^{2}}[/itex] 1≤x<2

F(x) = [itex]\frac{x^{2}}{24}[/itex] 2≤x≤4

So how can the CDF be negative for 1≤x<2, the CDF is P(X≤x), so to my mind that makes no sense. And secondly I have never seen a CDF with a discontinuity like in this one. At x=2, it jumps from -1/6 to 1/6

This made me think that I should ignore the negative sign in the CDF for 1≤x<2, but then for 1≤x<2 F(x) is a decreasing function, how canthatmake sense?

Someone enlighten me... please!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# CDF of a variable with a negative exponent in its PDF

**Physics Forums | Science Articles, Homework Help, Discussion**