Random variable probability problem

[thereddevils]

Homework Statement

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

Homework Equations

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 ?

 

[gerben]

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).

 

[thereddevils]

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).

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

?

 

[gerben]

yes exactly

 

[thereddevils]

yes exactly

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.