# Distribution Function Of X Help

mircat

## Main Question or Discussion Point

This is what I have:

Let the distribution function of X be given by
f(x) = 0, if x < (or equal to) 5
f(x) = x/10 - 1/2, if 5<x<(or equal to) 15
f(x) = 1, if x>15

Find p(6<x<12)

Ok, everyone. I need major help. I have no clue where to even begin. I have searched the web for help w/o luck. I need help in "layman's terms" as I do not understand any of this stuff. (note my other post on die rolls)LOL This equation is due tonight. Please, someone help me. Have to pass this class. Related Set Theory, Logic, Probability, Statistics News on Phys.org
Hurkyl
Staff Emeritus
Gold Member
I bet the answer (or at least a good starting point) lies in the definition of a probability distribution function, if you look it up in your textbook!

mircat
Lord, Hurky, I have. I have searched online, too. The book is a joke. No where in it is even a close example of one like this. I am still searching. Not going to give up just yet. )

Let say X is a continuous random variable with probability density function (or pdf) f(x), and cumulative density function (or distribution function df) F(x). By definition 0<=F(x)<=1, and lim F(x) as x goes to minus or infinity is 0 and 1 respectively. By the Fundamental Theorem of Calculus, f(x)=F'(x), then the integral of f(x)dx from a to b is equal to F(b)-F(a) (where a and b are constants within the interval where f(x) is defined).
In your case, just take the integration of F'(x) = d(x/10 - 1/2) = 1/10, with respect to x from 6 to 12. Or, just evaluate and compute F(12)-F(6)=[(12/10)-1/2] - [(6/10)-1/2].

I think this may work.

Last edited:
mircat
PS - only one week left, so I won't be pestering all you guys much longer! I really and truly appreciate everyone's help!!

Hurkyl
Staff Emeritus
Gold Member
Don't you have this definition of the probability distribution function:

f(a) := P(X < a)?

mircat
I have seen so many of these "formulas" it boggles my poor mind. This last week's assignment is more of the same type....density functions / continuous distribution functions. I just soooo don't get it. I really don't. I see an example from a lecture (written) then the problem I am given to do is nothing like it at all. An exaggeration is: f(x) = a x b + m (x)2 = v is what I am seeing in a lecture, but then I am told to solve the chemical equation for Tide. LOL Make sense? One paragraph shows Xs, Fs, maybe a Y - then the next one adds an E, H - w/o telling me why. Where'd the E and H come from? LOL I am trying to keep a sense of humor about all of this. I will let you know the final grade when it's over. ) Oh, I see a "t" on this week's lecture. ROFL!!! pami

ps - Hurky, did I tell you it's been almost 20 years since I've seen this stuff. I didn't even have to take Calculus/Stat/Prob in high school....so this is all foreign to me. )