Question

Question 4 Consider the following joint distribution of returns in Oil and Mining investments (as described in class slides for Chapter 4): Oil returns 10 5 0 -20 Mining returns marginal 0.20 0.16 0.10 0.02 0.48 0.08 0.26 0.12 0.06 0.52 marginal 0.28 0.42 0.22 0.08 1.00 where the entries in the central part of the matrice are the joint densities or frequencies. • Verify that Oil returns and Mining returns are not independent. • What is Pr(Oil return = 10 | Mining return = 8)? . What is Pr(Oil return = 10 Mining return = -2)? • What is Pr(Mining return = 8 Oil return = 10)? • What is Pr(Mining return = -2 Oil return = 10)?

Answer 1

Solution Mining 1 10 Oil Returns 5 o -20 Marginal Retwers | 0.20 0.16 0.10 0.02 0.48 0.08 0.26 0.12 0.06 0.52 Marginal 0.28 0.42 0.22 0.08 Now, Car The foremost condition of Independerue of two events A and B in P(ANB) = P(A).PCB). so to verify if oil Retwins and Mining Returns are independent or not, det us check for for the values when Mining Retwin = 8 and Oil Return = 10. P(Miring Retwen = 8, Oil Retwin = 10) = 0.20 PC Minining Return} = 8) = 0.48 Poil Retwen = 10) = 0.28. clearly. 0.20 40.48 x 0.28 Hence Mining Returns are not independent of oil Returns. (6) Ploil Return= 10 Mining Return 28) - P(Oil Returns cop Mining Retwen = 8) P(mining Return=8) [of A and B are two events, then PC AlB) - P4062] 0.20 0.48 0.42

c) PC or Returen slof meinining Retuon a-2) 1 = P( oil Return= 10 n Mining Return = -2) P( minining Return =~2) 0.08 0.52 0.15 d) P(Mining Return = 8 l oil Return = 10) :. = P( mining Return = 8 n Oil Retwin = 10) Ploil Return = 10) 0.20 0.28 0.71 e) PC Mining Return = -21 08 Return = 10). = P(meining Retwena 2, n Dil Retwin = 10) pCoil Return = 10) 0.08 0.28 0.29

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