Oscorp holds four types of mutual funds, A1, A2, As, and A. Shares of Ai account

Question

Oscorp holds four types of mutual funds, A1, A2, As, and A. Shares of Ai account for 40% of their shares in mutual funds. The other mutual funds account for the following percentages of their shares: A2, 15%; As, 10%; and A4,35%. An actuary determines that mutual fund A is two, three and four times more likely to have a return of over ten percent in 2018 than mutual funds A2, As and As, respectively. If at the end of 2018 a share of a mutual fund held by Oscorp has return of over ten percent determine the conditional probabilities of it being a share of Ai and of it being a share of A2.

Explanation / Answer

here let P(retun over 10%/type A1 fund) =x

P(return over 10%) =P(type A1 and return over 10%)+P(type A2 and return over 10%)+P(type A3 and return over 10%)+P(type A4 and return over 10%)

=0.4*x+0.15*x/2+0.1x/3+0.35x/4 =(143/240)x

hence conditional probabiltiy share A1 given return over 10%

=P(type A1 and return over 10%)/P(return over 10%) =0.4*x/(143x/240)=96/143

conditional probabiltiy share A2 given return over 10%

=P(type A2 and return over 10%)/P(return over 10%) =0.15*x/2/(143x/240)=18/143

Related Questions

Navigate

• Browse (All)
• Browse O
• Subjects

---

---

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