Each of 154 newly manufactured items is examined and the number of scratches per item is recorded (the items are supposed to be free of scratches), yielding the following data: number of scratches per item 0 1 2 3 4 5 6 7 observed frequency 14 40 43 25 10 15 4 3 let x = the number of scratches on a randomly chosen item, and assume that x has a poisson distribution with parameter μ. (a) find an unbiased estimator of μ and compute the estimate for the data. [hint: e(x) = μ for x poisson, so e(x) = ? ] (round your answer to two decimal places.) 1 (b) what is the standard deviation (standard error) of your estimator? compute the estimated standard error. [hint: σx2 = μ for x poisson.] (round your answer to three decimal places.)

10%

Explanation:

Since the bond is selling at a discount, it means that the coupon rate is blow the market rate, so the actual rate must be higher. Since there is only one option with an interest rate above 9%, we must check to see if it works.

10% yearly interest rate = 5% semiannual interest rate

we must determine the PV of the 20 coupons paid and the face value at maturity.

to calculate the PV of the 20 coupons ($45 each) we can use an excel spreadsheet and the NPV function with a 5% discount rate: PV of the coupons = $560.80

the PV of the face value in 10 years = $1,000 / 1.05²⁰ = $376.89

the present value of the coupons and the bond at maturity = $560.80 + $376.89 = $937.69. The PV using a 5% semiannual rate is very similar to $937.75, and since the question asked us to round up to the nearest whole percent, we can assume it is correct.