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

• laura_a
In summary, the conversation discusses finding the probability of an inequality involving a continuous random variable with a given probability density function. The suggested approach is to break the absolute value into two parts and integrate the pdf to find the total probability. This method is then further explained and appreciated by the person seeking help.
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

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

Wow! Thanks heaps warren that is great help!

## What is the meaning of P(|Y - 1/2| > 1/4)?

This is a statistical notation that represents the probability of the absolute difference between a random variable Y and the value 1/2 being greater than 1/4.

## How is P(|Y - 1/2| > 1/4) calculated?

To calculate this probability, you would need to know the distribution of the random variable Y and then use the appropriate formula. This calculation typically involves finding the area under a curve using integration or using a statistical software program.

## What does P(|Y - 1/2| > 1/4) tell us about the data?

This probability can provide information about the spread or variability of the data. A higher probability indicates a larger spread, while a lower probability indicates a smaller spread.

## Why is the value 1/4 used in the notation P(|Y - 1/2| > 1/4)?

The value 1/4 is used as a threshold to determine if the absolute difference between the random variable Y and 1/2 is considered large or small. This value can be adjusted depending on the specific research question or context.

## Can P(|Y - 1/2| > 1/4) be interpreted as a measure of central tendency?

No, this notation does not represent a measure of central tendency. It is a measure of spread or variability in the data.

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