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

[laura_a]

Homework Statement

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)

Homework Equations

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

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

 

[chroot]

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

 

[laura_a]

Wow! Thanks heaps warren that is great help!