Dice tosses are driving me insane (some stats help please)
So I need to know what the probability is for a number to be the middle number of 5 tosses (If the tosses are 1,3,6,4,5 then we order them 1,3,4,5,6 and the number I'm looking for is 4). I know that I have to take into account the probability that two numbers are less than or equal to the middle number P(X<= x), the probability of one number being equal to the middle number P(X = x), and the probability that two numbers are larger than the middle number P(X >=x).
I figured out that P(X<=x) = x/6 P(X=x) = 1/6 and P(X>=x) = (1-(P(X<=(x-1)))=1-((x-1)/6) however I don't know how to put this together to form the p.m.f for the whole problem.
Posted Mar 25, 2012, 1:25 AM UTC
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