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A bag contains four balls, numbered 2, 4, 6, 8 but identical in all other respects. One ball is chosen at random and the number on it is denoted by N, so that P(N=2) = P(N=4) = P(N=6) = P(N=8) = ;. Show that u = E(N) = 5 and o² = Var(N) = 5. %3D %3D %3D Two balls are chosen at random one after the other, with the first ball being replaced after it has been drawn. Let N be the arithmetic mean of the numbers on the two balls. List the possible values of N and their probabilities of being obtained. Hence evaluate E(N) and Var(N).

A bag contains four balls, numbered 2, 4, 6, 8 but identical in all other respects. One ball is chosen at random and the number on it is denoted by N, so that P(N=2) = P(N=4) = P(N=6) = P(N=8) = ;. Show that u = E(N) = 5 and o² = Var(N) = 5. %3D %3D %3D Two balls are chosen at random one after the other, with the first ball being replaced after it has been drawn. Let N be the arithmetic mean of the numbers on the two balls. List the possible values of N and their probabilities of being obtained. Hence evaluate E(N) and Var(N).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
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8 A bag contains four balls, numbered 2, 4, 6, 8 but identical in all other respects. One ball is chosen at random and the number on it is denoted by N, so that P(N= 2) = P(N=4) = P(N= 6) = P(N=8) =. Show that u = E(N) = 5 and o? = Var(N) = 5. %3D Two balls are chosen at random one after the other, with the first ball being replaced after it has been drawn. Let N be the arithmetic mean of the numbers on the two balls. List the possible values of N and their probabilities of being obtained. Hence evaluate E(N) and Var(N).
Transcribed Image Text:8 A bag contains four balls, numbered 2, 4, 6, 8 but identical in all other respects. One ball is chosen at random and the number on it is denoted by N, so that P(N= 2) = P(N=4) = P(N= 6) = P(N=8) =. Show that u = E(N) = 5 and o? = Var(N) = 5. %3D Two balls are chosen at random one after the other, with the first ball being replaced after it has been drawn. Let N be the arithmetic mean of the numbers on the two balls. List the possible values of N and their probabilities of being obtained. Hence evaluate E(N) and Var(N).
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