# Probability of X being greater than Y for independent uniform variables

• magnifik
In summary, a uniform random variable is a type of probability distribution where every possible outcome has an equal chance of occurring. Unlike other distributions, it does not favor any particular outcome. The formula for calculating the probability of a specific value is P(x) = 1 / (b - a), and it is commonly used in scientific research and real-world situations.

#### magnifik

Let X and Y be independent and uniform on {1, 2, ... M}
Find P(X > Y)

so i know that P(X = x) = 1/M and P(Y = y) = 1/M
i don't understand how Find P(X > Y) = (M+1)/2M

Hi magnifik!

Suppose M=3.

Then we have the matrix:
Code:
X\Y   1  2  3
1     ≥
2     ≥  ≥
3     ≥  ≥  ≥

In how many cases is the condition satisfied?
And what is the total number of cases?

## What is a uniform random variable?

A uniform random variable is a type of probability distribution where every possible outcome has an equal chance of occurring. In other words, the probability of any specific value is the same as any other value within the range.

## How is a uniform random variable different from other probability distributions?

Unlike other distributions, such as the normal or binomial distributions, a uniform random variable does not favor any particular outcome. This means that all values within the range have an equal likelihood of occurring.

## What is the formula for calculating the probability of a specific value with a uniform random variable?

The formula for calculating the probability of a specific value with a uniform random variable is P(x) = 1 / (b - a), where a is the lower bound of the range and b is the upper bound. This formula assumes that all values within the range have an equal probability of occurring.

## How is a uniform random variable used in scientific research?

A uniform random variable is often used in scientific research to simulate random events or to select a random sample from a population. It is also used in statistical analysis to model certain types of data, such as continuous measurements.

## Can a uniform random variable be applied to real-world situations?

Yes, a uniform random variable can be applied to real-world situations. For example, it can be used to model the probability of a specific outcome in a game of chance or to generate random numbers for simulations. It is also commonly used in statistical analysis to test hypotheses and make predictions.