Question

In: Statistics and Probability

Suppose the possible values of X are {xi}, the possible values of Y are {yj}, and...

Suppose the possible values of X are {xi}, the possible values of Y are {yj}, and the possible values of X + Y are {zk}. Let Ak denote the set of all pairs of indices (i,j) such that xi+yj =zk;thatisAk ={(i,j):xi+yj =zk}
a. Argue that

b. Argue that

P{X+Y=zk}= ? P{X=xi,Y=yj} (i,j )∈Ak

E[X+Y]=? ? (xi+yj)P{X=xi,Y =yj} k (i,j )∈Ak

c. Using the formula in b, argue that E[X+Y]=??(xi+yj)P{X=xi,Y =yj}

ij

d. Show that
P(X =xi)=?P(X =xi,Y =yj),P(Y =yj)=?P(X =xi,Y =yj)

ji

e. ProvethatE[X+Y]=E[X]+E[Y]

Expert Solution

orchestra answered 1 year ago

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