1. Let X and Y be independent random variables, each taking the values -1 or 1 with probability1, and let Z = XY. Show that X, Y, and Z are pairwise independent. Are they independent?

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Answered: 1. Let X and Y be independent random…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (h) and "tails" (t) which we write hth, ttt, etc. For each outcome, let N be the random variable counting the number of tails in each outcome. For example, if the outcome is tth, then N (tth)=2. Suppose that the random variable X is defined in terms of N as follows: X=N²-2N-2. The values of X are given in the table below. Outcome ttt htt hhh tht tth hth hht thh Value of X 1 -2 -2 -2 -2 -3 -3 -3 Calculate the probabilities P (X=x) of the probability distribution of X. First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row. Value X of X P(X=x) 0 0 0 0 0 00 X Ś
Consider a discrete random variable X that can assume three values 1, 2, and k with respective probabilities 0.5, 0.25, and 0.3. If E(X) = 1.9, what is the value of k? Select one: а. 5 b. 2 с. 1 d. 3 e. 4

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1. Let X and Y be independent random variables, each taking the values -1 or 1 with probability , and let Z = XY. Show that X, Y, and Z are pairwise independent. Are they independent?