What is the APY for an account that has an annual interest rate of 4.21% and is compounded daily (n=365)? APY = (1 + 5)² - 1 -)
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- 4. The lifetime, in years, of a type of small electric motor operating under adverse conditions is T ~Γ(6, 3.6). Whenever the motor fails, it is replaced with another of the same type. Find theprobability that fewer than 6 motors fail within one year.6. Consider xn+1 = (1/3)(2xn - 9/xn2). Does it converge for any nonzero initial point? If so, to what values?Everyday, James reverses his car from his driveway on to the road in such a way that there is a very small probability P that his car will be involved in a collision. ( i) Show that the probability that there will be no collision in a five-day week is (1−P)^5 and state one assumption that is made in your answer. (iii) Let P = 0.001. Check that the Poisson approximation can be used, and find the approximate probability that James will avoid a collision in 500 days.
- 13.Show that the third-order Adams-Moulton formula is yn+1=yn+h12(5fn+1+8fn−fn−1).It is predicted that, t years from now, the population of a certain town will be P(t)= (t^2+5t+22)/(t+2) thousand people. What are the largest and smallest populations that this town will have during the next 8 years?B) Let dP/dt =.5P - 50. Find the equilibrium solution for P. Furthermore, determine whether P is intially increasing faster if the initial population is 120 or 200.
- The article “n-Nonane Hydroconversion on Ni and Pt Containing HMFI, HMOR and HBEA” (G. Kinger and H. Vinek, Applied Catalysis A: General, 2002:139–149) presents hydroconversion rates (in μmol/g · s) of n-nonane over both HMFI and HBEA catalysts. The results are as follows: HMFI: 0.43 0.93 1.91 2.56 3.72 6.19 11.00 HBEA: 0.73 1.12 1.24 2.93 Can you conclude that the mean rate differs between the two catalysts?An SRS of 100 flights by Speedy Airlines showed that 64 were on time. An SRS of 100 flights by Happy Airlines showed that 80 were on time. Let pS be the proportion of on-time flights for all Speedy Airline flights, and let pH be the proportion of all on-time flights for all Happy Airlines flights. Is there evidence of a difference in the on-time rate for the two airlines? To determine this, you test the hypotheses H0 : pS – pH 0, Ha : pS – pH 0. The P-value of your test is 0.0117. Which of the following is an appropriate interpretation of the P-value? a. If the on-time rates for the two airlines are equal, there is a 0.0117 probability of getting samples with a difference as far or farther from zero as these samples. b. If the on-time rates for the two airlines are not equal, the probability of getting samples with a difference as far or farther from zero as these samples is 0.9883. c. The probability of making a Type I error is 0.0117. d. The probability of making a Type II error…4) What number of drones N makes your second-morning observations as likely as possible?5) Assuming again that the probability that N = n is proportional to the probability of observing this specificdata on the second day, find again the smallest nmax so that P (N ≤ nmax) = 0.95.
- A life insurance salesman operates on the premise that the probability that a man reaching his sixtieth birthday will not live to his sixty-first birthday is 0.050.05. On visiting a holiday resort for seniors, he sells 1010 policies to men approaching their sixtieth birthdays. Each policy comes into effect on the birthday of the insured, and pays a fixed sum on death. All 1010 policies can be assumed to be mutually independent. Provide answers to the following to 3 decimal places.Part a)What is the expected number of policies that will pay out before the insured parties have reached age 61?Part b)What is the variance of the number of policies that will pay out before the insured parties have reached age 61?Part c)What is the probability that at least two policies will pay out before the insured parties have reached age 61?Let x~ possion(alpha). Show that E[x(x-1)(x-2)....(x-k)]=ak+11s thls ab50Iut3Iy or c0ndltl0naIIy c0nv3rg3nt? PI3as3 sh0w step by step. Thls ls a c0mblnatl0n 0f aIt3rnatlng and p s3rl3s.