Find the following values by using the Poisson formula a. P(X = 5|0= 2.3) b. P(X = 2|0= 3.9) P(X < 3|0= 4.1) 3. %3D С.
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- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.If n is 30 and p is 0.04. using the Poisson approximation to the Binomial, the P(X < 2) is equal to a 0.4101 b. 0 .2103 C 0.0867 d. 0 .8795The US divorce rate has been reported as 3.6 divorces per 1000 population. Assuming that this rate applies to a small community of just 500 people and it’s Poisson distributed, and that x = the number of divorces in this community during the coming year, determine the following : a. E(x) b. P(x=1) c. P(x=4) d. P(x6) e. P(2x5)
- A researcher hypothesizes that in a certain country the net annual growth of private sector purchases of government bonds, B, is positively related to the nominal rate of interest on the bonds, NI, and negatively related to the rate of inflation Π: Bt = a0 + a1NIt + a2Π t + ut Note that it may be hypothesized that B depends on the real rate of interest on bonds, R, where R = NI – Π. Using a sample of 56 annual observations, s/he estimates the following equations: (1) Bt = 0.43 + 0.90NIt - 0.97Πt R21 = 0.962, SSR1 = 2.20, QRESET(F1,52) = 16.6 (3.58) (8.80) (-1.05) (2) Bt = 0.44 + 0.94Rt R22 = 0.960, SSR2 = 2.22, QRESET(F1,53) = 0.9 (9.70) (16.7) (3) Bt = 0.44 + 1.14NIt SSR3 = 9.20, QRESET(F1,53) = 59.9 (8.84) (36.1) (4) NIt = 0.08 + 0.94Πt R24 = 0.997, SSR4 = 0.18, QRESET(F1,53) = 1.4…Given is the number of calls arriving at a telephone exchange by a Poisson process with the intensity λ= 5 calls per 10 minutes. The following question I have to compute: 1. Compute the probability that at least one call will arrive in the next twominutes. 2. Find the probability that either A [ no calls arrive in the next two minutes ] or B [ exactly two calls arrive in the next four minutes ] 3. Let X denote the number of calls arriving in two minutes and Y = X + 1. Compute E(Y2).Suppose the math tutoring lab sees 56 students on a typical Tuesday and that the number of students per day is Poisson distributed. a. Find P(X ≤ 43). What function or formula did you use to answer this question? On my TI-84 Plus, I did a PoissonCDF with Lambda = 56 and the x value = 43. This resulted in 0.04309... Was I correct in using the PoissonCDF, or should I have used the PoissonPDF? b. What is the probability that more than 60 students will come in next Tuesday? Likewise, on my TI-84 Plus, I did a PoissonCDF with Lambda = 60 and the x value = 56. This resulted in 0.7309... Was I correct in assuming that the Lambda is 60 and the x value is 56?
- Prove the following property of the compound Poisson process:1. E(xt) = λ t E(Y).For b there are two cases and for c I have to plug the initial data into the odeEveryday, 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.
- To increase egg production, a farmer decided to increase the number of times the lights in his henhouse were on. Ten hens were randomly selected, and the number of eggs each produced was recorded. After one week of lengthened light time, the same hens were monitored again. The data is given here. At α = 0.05, can it be concluded that the increased light time increased egg production? Hen 1 2 3 4 5 6 7 8 9 10 Before 4 3 8 7 6 4 9 7 6 5 After 6 5 9 7 4 5 10 6 9 6Determine the upper-tail critical value tα/2 in each of the following circumstances.The Beer-Lambert law relates the absorbance A of a solution to the concentration C of a species in solution by A = MLC, where L is the path length and M is the molar absorption coefficient. Assume that C = 1.25 ± 0.03 mol/cm3, L = 1.2 ± 0.1 cm, and A = 1.30 ± 0.05.a) Estimate M and find the uncertainty in the estimate.b) Which would provide a greater reduction in the uncertainty in M: reducing the uncertainty in C to 0.01 mol/cm³, reducing the uncertainty in L to 0.05 cm, or reducing the uncertainty in A to 0.01?
