You are faced with a counting problem in which the number of outcomes is infinite. The counting method you should use is:
Answer(s): D
If the number of outcomes is infinite, a counting method should not be used at all, and the question cannot be answered with counting methods. None of the above is the correct response.
A joint probability is expressed symbolically as:
Answer(s): C
A joint probability takes the form of P(AB), the probability that a an event A and an event B will both happen.
A bar owner in Wisconsin has just won the Illinois Big Lotto jackpot that pays $200 million dollars in 25 equal installments paid annually. The bar owner can either accept the annual payments starting today or receive a lump sum today, using a discount rate of 9% per year. If the bar owner chooses to accept the lump sum, how much will he receive today?
Answer(s): A
The annual lotto payments equal 200/25 = 8 million dollars per year. Since the payments start today, the cash stream equals a payment of 8 million dollars today and an ordinary annuity with 24 payments. Thus, the present value of the lotto equals 8 + 8/0.09*(1-1/(1.09^24)) = 85.65 million dollars.
A sample of size 600 is drawn from a population. The sample mean equals 329. The total width of the 99% confidence interval for the population mean is 893. The estimated population variance equals ________.
If z is the z-value corresponding to the specified confidence level, the sample mean is M and the standard deviation is D in a sample size N, the confidence interval is specified as [M - z*D/sqrt(N), M + z*D/sqrt(N)].Thus, the width of the interval equals 2*z*D/sqrt(N). In the present case, for the 99% confidence interval, the normal probability table gives z = 2.58. The sample standard deviation equals sqrt(893) = 29.88. Therefore, the width of the 99% interval is 2*2.58*29.88/sqrt(600) = 6.30.
The monthly compounded rate is 15% quoted on an annualized basis. The equivalent quarterly compounded rate is:
To solve such problems, think about investing a dollar for 1 year. The final amount should be the same under both the quotations. Under quarterly compounded rate, r, $1 grows to (1+r/4)^4 in 1 year. Under monthly compounding, it grows to (1+0.15/12)^12 = 1.1608. Since these two should be equal, we get (1+r/4)^4 = 1.1608, giving r = 15.19%. Note that the quarterly compounded rate must be larger than the monthly compounded rate, ruling out 14.8% automatically.
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