Two draws are made at random without replacement from the digits {1,2,3,4}. Let X1 be the first digit drawn and X2 the second.
Let M=max(X1,X2) and S=X1+X2.
a) Find ?(?).
b) Make a joint distribution table for M and S.
c) Use the table in Part b to find the distribution of M.
d) Find ?(?).
Two draws are made at random without replacement from the digits {1,2,3,4}.
Let X1 be the first digit drawn and X2 the second.
So, we make the combination as (X1,X2)
{(1, 2), (1,3), (1,4), (2,1), (2,3), (2,4), (3,1), (3,2), (3,4), (4,1), (4,2), (4,3)}
I had a 1/4 probability of choosing that one and then 1/3 probability of choosing that second.
For each combination, the probability is 1/12
M=max(X1,X2) = {2,3,4}
M | Probability |
2 | 1/6 |
3 | 1/3 |
4 | 1/2 |
S=X1+X2 = {3,4,5,6,7}
S | Probability |
3 | 1/6 |
4 | 1/6 |
5 | 1/3 |
6 | 1/6 |
7 | 1/6 |
a)
b)
M | ||||
S | 2 | 3 | 4 | Total |
3 | (1/6) | 0 | 0 | 1/6 |
4 | 0 | (1/6) | 0 | 1/6 |
5 | 0 | (1/6) | (1/6) | 1/3 |
6 | 0 | 0 | (1/6) | 1/6 |
7 | 0 | 0 | (1/6) | 1/6 |
Total | 1/6 | 1/3 | 1/2 | 1 |
c)
M | Probability |
2 | 1/6 |
3 | 1/3 |
4 | 1/2 |
d)
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