Joint distribution of a discrete random variable

[Yankel]

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 !

 

[I like Serena]

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.

 

[Yankel]

A little bit hard to count them all, but it works ! Thanks