Prob solved 2ndedition

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Prob solved 2ndedition

Introduction to Probability 2nd Edition Problem Solutions (last updated: 9/18/15)© Dimit ri p. Bertsekas and John N. TsitsiklisMassachusetts Institute

Prob solved 2ndedition e of TechnologyWWW site for book information and ordershttp://www.athena8c.oomAthena Scientific, Belmont, Massachusetts1c II A p T E K 1Solution to Pr

oblem 1.1. We haveA {2.4,6}, fi {4,5,6},so AUB = {2,4,5,6), and(Au fir {1.3}.On the other hand.A( Í1Ũ' = {1,3.5} n {1.2,3} = {1,3}.Similarly, we haw A Prob solved 2ndedition

n Ỡ{4,6), and(Anfif = {1,2.3,5}.On the other hand.ArUB' = {1.3, 5} u {1,2,3} = {1,2,3.5}.Solution to Problem 1.2. (a) By using a Venn diagram it can

Prob solved 2ndedition

be seen that for any sets s and 7’. we haves {5nT)U(Sn7^.(Alternatively, argue that any ;r must belong to either 7’ or to 7*, so X belongs to s if and

Introduction to Probability 2nd Edition Problem Solutions (last updated: 9/18/15)© Dimit ri p. Bertsekas and John N. TsitsiklisMassachusetts Institute

Prob solved 2ndedition he roles of A and fi to obtain the second relation.(I>) By De Morgan’s law, we haw(Anfif = .4‘utf,and by using the equalities of part (a), we obtain(A

nB)c = ((A'nBJuiA'nB'JJu^AnB'JupPnB*-)} = (A Prob solved 2ndedition

s://khothuvien.cori!andyfAlf = {2}, A' ị-iur = {4.6}. AHir = {5}.Thus, I he ixjuality of part (11) is verified.Solution to Problem 1.5. Let G' and c b

Prob solved 2ndedition

e the events that the chosen student is a genius and a chocolate lover. ns|Ki:l .ively. We have P(<7) = 11.6. P((?) = (1.7, ami P((7nC) = 11.4. We ant

Introduction to Probability 2nd Edition Problem Solutions (last updated: 9/18/15)© Dimit ri p. Bertsekas and John N. TsitsiklisMassachusetts Institute

Prob solved 2ndedition .Solution to Problem 1.6. We first determine the probabilities of the six possible outcomes. Let a P({!}) = P({3}) = p({5}) and b = P({2}) = P({1}) =

P({6}). We are given that 6 2a. By the additivity and normalization axioms. 1 = 3a 4 36 3a + 6a = 9a. Thus, 0=1/96 = 2/9. and P({1,2.3}) = 4/9.Solut i Prob solved 2ndedition

on to Problem 1.7. The outcome of this experiment can be any finite sequence of the form (ai,a2,...,an), where n is an arbitrary positive integer, 01,

Prob solved 2ndedition

02......a„ 1

Introduction to Probability 2nd Edition Problem Solutions (last updated: 9/18/15)© Dimit ri p. Bertsekas and John N. TsitsiklisMassachusetts Institute