Consider the distribution A - B. What is its mean? What is its Standard Deviation? What is p(A-B>0)?
I have two similar (but not identical) normal distrubutions. Let's say distribution "A" has a mean of a and an SD of A, and distribution "B" has a mean of b and an SD of B. QUESTION: What is the probability that a score from distribution A will be greater than a score from distribution B? Is there a formula in terms of a,b,A and B?
Thanks for that. Got it sorted. Now I'm up against the next stage question. Consider 3 teams (A,B & C) in a league. The probability that A finishes the season higher than B is P1 and the probability that A finishes higher than C is P2. Q: What is the probability (P3) that A finishes higher in the league than BOTH B & C? (I know that the answer is not P1 x P2 by considering the case of 3 equal teams where you would have P1 = 0.5, P2 = 0.5 and P3 = 0.3333)
Should we be on a different thread?
How about something in the neighborhood of this: p(A>B|B>C) + p(A>C|C>B). Of course, one would want to generalize this before attempting too many teams.
My maths degree is 25 years ago and I'm struggling with your notation. How do I actually calculate p(A>B|B>C) - (it cannot just be 0.5 x 0.5 becasue this would give a final answer of 0.25 + 0.25 = 0.5 for 3 equal teams which is clearly incorrect.
Sorry to be a pain!
Read p(A>C|B>C) "the probability that A finishes higher than C, given that B finished higher than C."
Off the top of my head, it does not appear to be enough information. I'm looking for p(B>C) or p(C>B) and we've neither.
Alternatively, you could hald a tournament. There are only three games.
A plays B
A plays C
B plays C
Each team has only two games and this, three outcomes (0,2), (1,1), (2,0). Can you assign probabilities to these outcomes?
OK, thank you. I understand the "given that" concept. P(B>C) is 1-P(C>B) and lets call this P3 for the general situation. As stated earlier P1 is P(A>B) and P2 is P(A>C). So the question is:
What is P(A> both B & C) in terms of P1, P2 and P3?
A simulated tornament is tricky. In the situation I'm trying to grasp, teams A,B,C are any three chosen teams from a league with many more teams in it, and P1, P2, P3 are calulated using your previous help on comparing normal distributions.
Please ignore earlier notation where I used "P3" to donote the answer.