Let:
f(x) = { cx^2 for 0<=x<=3
{0, else


It wants me to find c, and I really have no idea how to find c...
Can anyone help?
Thanks.

me thinks your missing some info.

yup

also, is c a constant?

doesn't look like stats btw

This post was edited by zackill4 on Sep 30 2013 11:18am

Well, later it asks for us to find F(x), the CDF, E(x), VAR(x), and stuff. But that's all it gives me for the first part.
We're supposed to use Integration at some point, I think to find the CDF (or F(x)), but yeah.
That's all it gives, which is why I am confused.

/e When I get home I will take a picture and put it up here.

This post was edited by furbyjs on Sep 30 2013 11:58am

lol dude, you forgot to tell us that this is a probability distribution function (pdf)

that does make it stats after all I guess... but it's not something we could have figured out with what you had given

the integration of your function from 0 to 3 must be equal to 1 to be a valid pdf

therefore integral(cx^2) from 0 to 3 equals 1

c/3*x^3 from 0 to 3 = 1

c27/3-0 = 1

c = 1/9


please check my work of course

This post was edited by zackill4 on Sep 30 2013 12:05pm

I'll try to sorta explain how this stuff works.

The pdf tells you the probability a random variable (RV) take on a particular value (ie P(X = x), where X is a RV, and x is a particular value)

The probability X takes on any value must be 1 (100%). This probability is the sum of all P(X=x) for all possible values of x.

For a continuous pdf, this "sum" must be calculated as an integral, the integral of the pdf from neg infinity to infinity. In your case, the pdf takes on 0 everywhere except [0,3], so you only need to integrate from 0 to 3.

If you want the probability X < c, you must sum all probabilities P(X=x) for all x < c. P(X < c) is the same as F(c), where F is the CDF. With a continuous pdf, this "sum" is again found by integrating, this time integrating the pdf from negative infinity to c. Note that in your case, for a c = 3, the CDF should return 1 to reflect that < 3 covers all possible values RV X can take.



Edit: I suggest you re-read the chapter or your lecture notes on this topic. If you are unsure where integrals come into play here and you need to find the CDF, expected value, and variance, then you are completely lost. All 3 are done with integration.

This post was edited by zackill4 on Sep 30 2013 12:30pm

Thanks, I appreciate it. I understand how they work, it just didn't occur to me to set the integral equal to zero. Thanks though, that's exactly what I was looking for.

/e Equal to one I meant xD

This post was edited by furbyjs on Sep 30 2013 05:14pm

haha ok, sounds good! It's a trick that they'll probably quiz you on a million times