Distribution Function Of X Help

[mircat]

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.

 

[Hurkyl]

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. )

 

[jetoso]

Answer

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.

 

[mircat]

Oh, thank you! I found this site that I have been looking at http://www.mathsnet.net/asa2/modules/s22verify.html for help, too. I think you have explained it a bit better. Thank you!

 

[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]

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. )