Joint PMF (calculating probabilities)

thumper88

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Joined
Apr 3, 2012
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So I have a problem that says four fair dice are rolled. So that tells me 64 sample space.
X is the number of fives observed and Y is the number of sixes observed.
I created a table
PX,Y(x,y)y=0y=1y=2y=3y=4PX(x)
x=0
x=10
x=200
x=3000
x=40000
PY(y)


I understand the method of calculating the PMF, I'm having counting issues, calculating the probability for each part. I believe the zeros are placed correctly? If 4 fives are observed you can't have more than 0 sixes observed and vice versa.
For example, how do I calculate the probability of 2 fives observed and 2 sixes observed? Please help, thanks.
 
So I have a problem that says four fair dice are rolled. So that tells me 64 sample space.
X is the number of fives observed and Y is the number of sixes observed.
LaTeX is down so a fancy answer is out of the question .
Let #(x=m,y=n) mean the number of 4-tuples in which there are m fives and n sixes.
#(x=0,y=0)=44 ,

#(x=1,y=2)=(4!/2)(4)=2(4!).

#(x=2,y=2)=6

You try the rest.
 
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