1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Random variable probability problem

  1. Sep 7, 2010 #1
    1. The problem statement, all variables and given/known data

    Continuous random variable X has probability density function defined as

    f(x)= 1/4 , -1<x<3

    =0 , otherwise

    Continuous random variable Y is defined by Y=X^2

    Find G(y), the cummulative distribution function of Y

    2. Relevant equations



    3. The attempt at a solution

    G(y) = P(-sqrt(y)<=X<=sqrt(y))

    What does this mean? G(Y) is defined as P(-sqrt(y)<=X<=sqrt(y)) for 0<=X<=9 ?
     
  2. jcsd
  3. Sep 7, 2010 #2
    Re: probability

    G(y), the cummulative probability distribution function of Y, is a function that gives the probability that Y is smaller than y.

    P(-sqrt(Y)<=X<=sqrt(Y)) is a way of writing: Probability that X is in between plus and minus the square root of Y (note the use of capital Y here, y and Y are not the same thing).
     
  4. Sep 7, 2010 #3
    Re: probability

    Thanks Gerben, the next step will be to integrate the pdf?

    ie [tex]G(y)=\int^{\sqrt{y}}_{-\sqrt{y}}\frac{1}{4}dx[/tex] for [tex]0\leq y\leq 9 [/tex]

    ?
     
  5. Sep 7, 2010 #4
    Re: probability

    yes exactly
     
  6. Sep 10, 2010 #5
    Re: probability

    There will be 3 cases here,

    case 1 : G(y)=0 for y<0

    case 2 : G(y)= integration from -sqrt(y) to sqrt(y) 1/4 dx for 0<=y<=9

    case 3: G(y)=1, for y>9

    Is this the domain? I doubt my domain for case 2 is correct.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook