# Homework Help: Random variable probability problem

1. Sep 7, 2010

### thereddevils

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. Sep 7, 2010

### gerben

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).

3. Sep 7, 2010

### thereddevils

Re: probability

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

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

?

4. Sep 7, 2010

### gerben

Re: probability

yes exactly

5. Sep 10, 2010

### thereddevils

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.