What does this mean? P(|Y - 1/2| > 1/4)? (2nd year stats)

1. Feb 11, 2008

laura_a

1. The problem statement, all variables and given/known data

The question is

Let Y be a continuous random variable with pdf f_Y(y) = 3(1-y)^2

and I have to find P(|Y - 1/2| > 1/4)

2. Relevant equations

Is there a formula involved here or something that can help me???

3. The attempt at a solution

I'm not even sure how to find the probability of a pdf once it's given, is there a formula that I can use and plug the values in... I think it's more confusing that there is an inequality in the probability as well... any hints will be greatly appreciated

2. Feb 11, 2008

chroot

Staff Emeritus
Well, break the absolute value into two parts first.

If you're looking for the region where | Y - 1/2 | > 1/4, that's the same as looking for the combined areas where Y - 1/2 > 1/4 and where -( Y - 1/2 ) > 1/4.

In other words, you need to find the total probability that Y > 3/4, added to the total probability that Y < 1/4. Both of these total probabilities can be found by integrating the pdf.

- Warren

3. Feb 11, 2008

laura_a

Wow!! Thanks heaps warren that is great help!