Suppose the probability that oil prices will rise any given quarter is 0.51, and the probability that oil prices will stay level or decline is 0.49. If oil prices rise, GNP will contract by 1% with 80% probability, and expand by 0.5% with 20% probability. If oil prices decline or stay level, GNP will expand 3% with a 75% probability and contract 0.5% with a 25% probability. What is the expected change in GNP in the next quarter?
Answer(s): A
We need the total probability rule for expected value, for which the formula is E(X) = E(X | S_1) * P(S_1) + E(X | S_2) * P(S_2) + ... + E(X |S_n) * P(S_n). Here, E(X) is the expected change in GNP. S_1 is the event that oil prices rise, and S_2 is the event that oil prices fall. Therefore, E(X) = 0.51 * (- 1%*80% + 0.5%*20%) + 0.49 * (3%*75% - 0.5%*25%) = 0.68%, an expansion.
If you already have $500 in a savings account, how much must you deposit 4 years from now in order to have $5,000 in 8 years, assuming the account earns interest at 10% per year, compounded annually?
Answer(s): C
The way to approach this question is to find the PV today of the $5,000 amount, determine the difference between this PV and the existing $500 amount in the account, and then move this difference out to the 4 year from now point. On the BAII Plus, press 8 N, 10 I/Y, 0 PMT, 5000 FV, CPT PV. Then press + 500 =. Then press PV, 4 N, CPT FV to see the answer. On the HP12C, press 8 n, 10 i, 0 PMT, 5000 FV, PV. Then press 500 +.Then press PV, 4 n, FV to see the answer. Make sure the BAII Plus has the P/Y value set to 1.
The joint probability of events A and B occurring equals 0.11. The probability of neither A nor B occurring equals 0.64. If P(A) equals 0.24, the probability of B occurring equals ________.
Answer(s): D
We are given that P(neither A nor B) = 0.64, P(A and B) = 0.11 and P(A) = 0.24. The probability of neither A nor B occurring equals one minus the probability of either A or B occurring i.e. P(neither A nor B) = 1 - P(A or B).Thus, P(A or B) = 1 - P(neither A nor B) = 1 - 0.64 = 0.36.Now, P(A or B) = P(A) + P(B) - P(A and B)Therefore, P(B) = P(A or B) - P(A) + P(A and B) = 0.36 - 0.24 + 0.11 = 0.23.
Which of the following is/are true?
Answer(s): E
By definition, there are as many values above the median as below it. Each sample has a unique median. (II) and (III) hold for the mean, not for the median.
If you deposit $150 a month, beginning next month, for 20 years into an account paying 6% per year, compounded monthly, how much is in your account after the last deposit?
On the BAII Plus, press 240 N, 6 divide 12 = I/Y, 0 PV, 150 PMT, CPT FV. On the HP12C, press 240 n, 6 ENTER 12 divide i, 0 PV, 150 PMT, FV. On the BAII Plus, make sure the value of P/Y is set to 1. Note that the answer is displayed as a negative number.
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