There are 5 boxes. One box is empty; two boxes each contains one marble; and the...

There are 5 boxes. One box is empty; two boxes each contains one marble; and the remaining two boxes each contains two marbles. Suppose that the colors of the marbles are not known, but it is known that each marble can only be either red or green, with equal probability. Suppose that ONE box is randomly chosen from the 5 boxes, and let R denote the number of the red marble(s) the box has, and G be the number of the green marble(s) the box has. (Of course either R or G, or both, can be 0.)

(a) Write out the joint probability distribution of R and G.

(b) P(R > 0 ) = ?

(d) P(G=1 | R=1) = ?

(e) E[R | G=1] = ?

(f) Are R and G independent? (Yes or no, you must justify your answer mathematically; otherwise, no credits can be given.)

(g) Calculate the correlation between R and G.

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Expert Solution

orchestra answered 1 year ago

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