
#1
May1012, 07:03 AM

P: 81

I was looking to a video about cumulative distribution function (http://www.youtube.com/watch?v=658WXDkhU_w) and he show the following function:
[itex] \ \ \ \ \ \ \ \ \ \ \ \ \ \ \  1/4, 0 \leq x \leq1 \\ f(x) =<(x^3)/5, 1 \leq x \leq 2 \\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0, otherwise.[/itex] At minute 8:45, he presents the cumulative distribution as: [itex] \ \ \ \ \ \ \ \ \ \ \ \ \ \ \  0, x \leq 0 \\ F(x) = < \frac{1}{4}x, 0 \leq x \leq 1 \\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \  \frac{1}{20}(x^4+4), 1 \leq x \leq 2 \\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \  1, \ x \geq 2 [/itex] I don't understand why F(x) is 1 for [itex]x \geq 2 [/itex], if f(x) is 0, otherwise. Why? BTW, I hope that that my functions are legibles, because I don't know how to put big curly brackets. 



#2
May1012, 10:39 AM

Sci Advisor
P: 3,173





#3
May1112, 03:54 AM

P: 81

I understand what you said, but the probability of happening 3 is 0, because it's not defined in f(x). For me, F(3) should never be defined.




#4
May1112, 07:27 PM

Sci Advisor
P: 3,173

cumulative distributed function example 



#5
May1112, 07:48 PM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 38,882

If f(x) is the "probability density function" then [itex]F(X)= \int_{\infty}^X f(x)dx[/itex] is the probability that x is less than or equal to X. 


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