27·\"Let the sample space S = {aaa bbb, coc, abc, bca, cba, acb, bac, cab), and

Question

27·"Let the sample space S = {aaa bbb, coc, abc, bca, cba, acb, bac, cab), and let the prob ability that each element of S occurs is 1/9. (That is, all outcomes are equally likely.) Let the event A, be the event that the ith place in the triple is is, A is the event that the outcome is aaa, abc, or acb, since the first place is occupied by a in these outcomes. Also, the event A1 n A2 would mean that both the first and second places in the triple are occupied by a occupied by a. That Calculate PIA), P[A2), P[A3j, and PAi n A2), PAi n As], P[A2 n A3], and PtAinA2nA3. Use the definitions of pairwise independence and mutual independence to determine whether the events A1, A2, and Ag are pairwise independent or mutually independent. In the writeup of your answer, fully justify your arguments (use the definitions!)

Explanation / Answer

here event in A1 ={aaa ; abc; acb}

hence P(A1) =3/9 =1/3

event in A2 ={aaa ; bac; cab}

P(A2) =3/9 =1/3

event in A3 ={aaa ; bca; cba}

P(A3) =3/9 =1/3

event in (A1nA2) ={aaa}

P(A1nA2) =1/9

event in (A1nA3) ={aaa}

P(A1nA3) =1/9

event in (A2nA3) ={aaa}

P(A2nA3) =1/9

event in (A1nA2nA3) ={aaa}

P(A1nA2nA3) =1/9

as P(A1nA2) =P(A1)*P(A2) =1/9

also P(A1nA3) =P(A1)*P(A3) =1/9

P(A2nA3) =P(A2)*P(A3) =1/9

but P(A1nA2nA3) is not equal to P(A1)*P(A2)*P(A3)

therefore A1 ; A2 and A3 are not pairwise independent but mutually independent.

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.