Two ballpoint pens are selected at random from a box that contains 3 blue pens, 2...

 

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Two ballpoint pens are selected at random from a box that contains 3 blue pens, 2 red pends, and 3 green pens, If X is the number of blue pens selected and Y is the number of red pens selected, find (a) the joint probability function f(x,y), (b) Show that the column and row tables of (a) give the marginal distributions of X alone and of Y alone. (c) P{(X,Y) = A}, where A is the region P{(X,Y)|x+y1}. (d) Find the conditional distribution of X, given that Y=1, use it to determine P{X=0|Y=1} (e) Find the covariance of X and Y. Two ballpoint pens are selected at random from a box that contains 3 blue pens, 2 red pends, and 3 green pens, If X is the number of blue pens selected and Y is the number of red pens selected, find (a) the joint probability function f(x,y), (b) Show that the column and row tables of (a) give the marginal distributions of X alone and of Y alone. (c) P{(X,Y) = A}, where A is the region P{(X,Y)|x+y1}. (d) Find the conditional distribution of X, given that Y=1, use it to determine P{X=0|Y=1} (e) Find the covariance of X and Y.