MHB Joint distribution of a discrete random variable

AI Thread Summary
The discussion revolves around calculating the joint distribution of two random variables, X (the minimum number drawn) and Y (the maximum number drawn) from an urn containing six numbered balls. The user seeks to determine the probabilities for specific outcomes, such as X = 1 and Y = 5, and X = 2 and Y = 6. A suggested method for solving this is to enumerate all possible combinations of drawing four balls from the six, which totals 15 combinations. This approach, while potentially tedious, provides a systematic way to calculate the desired probabilities. Understanding the joint distribution requires careful consideration of the relationships between the values of X and Y based on the drawn combinations.
Yankel
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Hello all

I have this question I am trying to solve.

In an urn there are 6 balls, numbered: 1,2,3,4,5,6. We take 4 balls outs, without replacement.

X - the minimal number we see
Y - the maximal number we see

I need to joint distribution.

I understand that X is getting the values 1,2,3 while Y 4,5,6.

The problem is calculating the probabilities. How do I calculate the probability that X = 1 and Y = 5 ? What about the probability that X = 2 and Y = 6 ? And so on...

thanks !
 
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Yankel said:
Hello all

I have this question I am trying to solve.

In an urn there are 6 balls, numbered: 1,2,3,4,5,6. We take 4 balls outs, without replacement.

X - the minimal number we see
Y - the maximal number we see

I need to joint distribution.

I understand that X is getting the values 1,2,3 while Y 4,5,6.

The problem is calculating the probabilities. How do I calculate the probability that X = 1 and Y = 5 ? What about the probability that X = 2 and Y = 6 ? And so on...

thanks !

Hi Yankel,

How about enumerating them all?
There are only $\binom 6 4 = 15$ possible combinations.
 
A little bit hard to count them all, but it works ! Thanks
 
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