Applied Statistics

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Consider a box of tickets where each ticket has exactly one number on it. Suppose further that the average of the ticket numbers in the box is 0. Now take each ticket, erase the original number and write a new number in it's place which equals 2 plus the original number. Now randomly pick a ticket and let X denote the number showing. What is E(X)? Let X be a random draw from the following list of 8 num- bers: 0, -1, -1, 1, 1, 1, 1, 1. What is var (X )?Suppose Z is a random variable with probability mass function 1/3 if z = 1 p z) = 1/3 if z = 2 1/3 if z = 3 (a) What is the expected value of Z? (b) Compute the PMF of Z2. (c) Compute the PMF of (Z - E(Z) )2.\f(Added April 14) Suppose X is a random variable with PMF given by the following table px 0.4 0.1 0.2 0.3 Find P(X = 1/X