glass ocean
so i am done with a)
but b) I don't understand what is mean't by max(X,Y)?
so I got p(0)=1/8, p(1)=3/8, p(2)=3/8 and p(3) = 1/8
that would be the case for both X and Y since its a fair coin
so would P(M) just look the same?
Since:
P(X=0)=P(Y=0)=1/8?
am I missunderstand something here?
glossy path
so i am done with a)
but b) I don't understand what is mean't by max(X,Y)?
so I ...
(b)
max(X, Y) is a random variable equal to the maximum of X and Y. Also note that X + Y = 3, so Y = 3 - X, so M = max(X, 3 - X).
Since the support of both X and Y is {0, 1, 2, 3}, the support of M must be just {2, 3}. So:
P(M = 2) = P(max(X, 3 - X) = 2) = P(X = 1) + P(X = 2)
P(M = 3) = P(max(X, 3 - X) = 3) = P(X = 0) + P(X = 3)
Calculate these probabilties to find the law of M.
(c)
Again, note that Y = 3 - X, so X - Y = X - (3 - X) = 2X - 3.
glass ocean
(b)
max(X, Y) is a random variable equal to the maximum of X and Y. Also note th...
much thanks. i loved your explanation. just a small inquiry, why is it that you do P(M=2) = P(X=1) + P(X=2)? It is the x's which result in P(M=2)? Since they are disjoint events we can add their respective probabilities?
leaden oceanBOT
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