# Probability question - calculating marginal pdfs

• jaejoon89
In summary, probability is a measure of the likelihood of an event occurring and is expressed as a number between 0 and 1. A marginal probability distribution shows the probabilities of each outcome for one variable, regardless of other variables. To calculate marginal pdfs, one needs to integrate the joint pdf over all possible values of the other variables. A marginal pdf displays probabilities for one variable, while a conditional pdf shows probabilities for one variable given a specific value of another variable. Marginal pdfs are important in probability as they allow for the analysis of a single variable and the calculation of specific probabilities for that variable.
jaejoon89

## Homework Statement

Calculate the marginal probability distribution function of X given joint pdf

f(x,y) = 15x^2 y for 0 <= x <= y <= 1
f(x,y) = 0 otherwise

## Homework Equations

f_x (x) = integral of f(x,y) dy

## The Attempt at a Solution

I've got no idea what the bounds are for this integral.

Also, would it be easier to do it in polar coordinates?

0<=x<=y<=1. For a fixed value of x, doesn't y go from x to 1? I'm not sure why this is confusing you and I don't think polar coordinates will help one bit.

## 1. What is probability?

Probability is a measure of the likelihood that an event will occur. It is expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty.

## 2. What is a marginal probability distribution?

A marginal probability distribution is a probability distribution that shows the probabilities of each outcome for one variable, regardless of the values of other variables.

## 3. How do you calculate marginal pdfs?

To calculate marginal pdfs, you need to integrate the joint pdf (probability density function) over all possible values of the other variables.

## 4. What is the difference between a marginal pdf and a conditional pdf?

A marginal pdf shows the probabilities of one variable, while a conditional pdf shows the probabilities of one variable given a specific value of another variable.

## 5. Why are marginal pdfs important in probability?

Marginal pdfs are important because they allow us to analyze the distribution of a single variable, without considering the influence of other variables. They also help us to calculate probabilities for specific events or ranges of values for that variable.

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