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2) Assume that X is the random number we obtain when we throw a certain given four sided die. So, the random number X is either 1, 2, 3 or 4 each with a given probability denotes by P1. P2. Pa. P4. Hence P(X = 1) = pi and P(X = 2) = p2,. Assume that we throw this die many times independently. Show (prove) that the average goes to the expectation. that is show that X1 + X2+... +X + E[X] as n goes to infinity. For this you can assume known, the fact that the relative frequencies with which each side appears on the long run converges to the probability of the respective side

2) Assume that X is the random number we obtain when we throw a certain given four sided die. So, the random number X is either 1, 2, 3 or 4 each with a given probability denotes by P1. P2. Pa. P4. Hence P(X = 1) = pi and P(X = 2) = p2,. Assume that we throw this die many times independently. Show (prove) that the average goes to the expectation. that is show that X1 + X2+... +X + E[X] as n goes to infinity. For this you can assume known, the fact that the relative frequencies with which each side appears on the long run converges to the probability of the respective side

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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2) Assume that X is the random number we obtain when we throw a certain given four sided die. So, the random mumber X is either 1, 2, 3 or 4 each with a given probability denotes by P1. P2. P3, Pa. Hence P(X = 1) = pi and P(X = 2) = p2,.Assume that we throw this die many times independently. Show (prove) that the average goes to the expectation. that is show that X1 + X2 +... +Xn + E[X] as n goes to infinity. For this you can assume known, the fact that the relative frequencies with which each side appears on the long run converges to the probability of the respective side
Transcribed Image Text:2) Assume that X is the random number we obtain when we throw a certain given four sided die. So, the random mumber X is either 1, 2, 3 or 4 each with a given probability denotes by P1. P2. P3, Pa. Hence P(X = 1) = pi and P(X = 2) = p2,.Assume that we throw this die many times independently. Show (prove) that the average goes to the expectation. that is show that X1 + X2 +... +Xn + E[X] as n goes to infinity. For this you can assume known, the fact that the relative frequencies with which each side appears on the long run converges to the probability of the respective side
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