Notation for Probability Distribution of Two Dice Rolls

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Discussion Overview

The discussion revolves around defining a random variable related to the outcome of rolling two dice, specifically focusing on how to mathematically express the concept of taking the larger value of the two rolls or the same value if they are equal. The scope includes mathematical notation and probability distribution formulation.

Discussion Character

  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • Claudius seeks assistance in expressing the definition of the random variable X, which is the larger of two dice rolls or the same value if the rolls are equal.
  • Claudius has already solved the probability distribution question but is focused on the mathematical expression of the random variable.
  • Another participant suggests using the notation U = MAX(X,Y) to represent the random variable, where X and Y are the outcomes of the dice rolls, each uniformly distributed from 1 to 6.
  • The same participant mentions the use of conditional probabilities to derive the final distribution for U.

Areas of Agreement / Disagreement

Participants do not appear to disagree, but the discussion remains focused on the mathematical expression rather than reaching a consensus on the final probability distribution.

Contextual Notes

The discussion does not resolve the specific mathematical notation for the random variable X, and there may be additional assumptions regarding the interpretation of the maximum function and the distribution of the dice rolls that are not explicitly stated.

Iclaudius
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Hello friends,

I have this problem it reads:

A random variable X is defined to be the larger of the two values when two dice are thrown, or the value if the values are the same. Find the probability distribution for X.

So I don't know how to state "X is defined to be the larger of the two values when two dice are thrown, or the value if the values are the same" mathematically. If someone could tell me, it would be much appreciated.

Thank you for you time,
Claudius
 
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Note - I have already solved this question just want to know how to express that above statement in math.
 
Iclaudius said:
Note - I have already solved this question just want to know how to express that above statement in math.

Do you know how to write conditional probabilities?
 
Iclaudius said:
Note - I have already solved this question just want to know how to express that above statement in math.

Lets say your random variable U takes the maximum value of X and Y.

You can write this mathematically as

U = MAX(X,Y), X ~ U(1,6) [Discrete], Y ~ U(1,6) [Discrete].

As for the distribution you can use SW VandeCarr's hint and list conditional probabilities to get a final distribution for U.
 
ah ok
 
Last edited:

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