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!

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

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