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Random variable probability problem

  • #1
438
0

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 ?
 

Answers and Replies

  • #2
508
1


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
438
0


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

?
 
  • #4
508
1


yes exactly
 
  • #5
438
0


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.
 

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