# Question: Suppose the possible values of X are xi the possible

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; that is,

Ak = {(i, j): xi + yj = zk}.

(a) Argue that

(b) Show that

(c) Using the formula from part (b), argue that

(d) Show that

(e) Prove that

E[X + Y] = E[X] + E[Y]

Ak = {(i, j): xi + yj = zk}.

(a) Argue that

(b) Show that

(c) Using the formula from part (b), argue that

(d) Show that

(e) Prove that

E[X + Y] = E[X] + E[Y]

## Answer to relevant Questions

Let X be such that P{X = 1} = p = 1 − P{X = −1} Find c ≠ 1 such that E[cX] = 1. Trains headed for destination A arrive at the train station at 15-minute intervals starting at 7 A.M., whereas trains headed for destination B arrive at 15-minute intervals starting at 7:05 A.M. (a) If a certain passenger ...A system consisting of one original unit plus a spare can function for a random amount of time X. If the density of X is given (in units of months) by what is the probability that the system functions for at least 5 months? A model for the movement of a stock supposes that if the present price of the stock is s, then, after one period, it will be either us with probability p or ds with probability 1 − p. Assuming that successive movements are ...Compute E[X] if X has a density function given by (a) (b) (c)Post your question