What is Poisson probability? What are 3 characteristics of Poisson probability?  What are 2 business applications of Poisson probability?  Calculate the Poisson probability for the following data. x = 3, lambda = 2 x = 2, lambda = 1.5 x = 12, lambda = 10 For the problem statements starting from question 6 onward, exercise caution when entering data into Microsoft Excel. It's essential to carefully evaluate which value represents x and which represents λ.  A call center receives an average of 3 calls per minute. What is the probability that exactly 5 calls are received in a given minute?  On average, 4 patients arrive at an emergency room every hour. What is the probability that exactly 7 patients will arrive in the next hour?  A production line produces an average of 2 defective items per hour. What is the probability that exactly 3 defective items will be produced in the next hour?  An intersection experiences an average of 1.5 accidents per month. What is the probability that…

(Nondiagonal Jordan form) Consider a linear system with a Jordan form that is non-diagonal. (a) Prove Proposition 6.3 by showing that if the system contains a real eigenvalue 入 = O with a nontrivial Jordan block, then there exists an initial condition with a solution that grows in time. (b) Extend this argument to the case of complex eigenvalues with Reλ = 0 by using the block Jordan form Ji = 0 W 0 0 3000 1 0 0 1 0 ω 31 0

You manage a chemical company with 2 warehouses. The following quantities of Important Chemical A have arrived from an international supplier at 3 different ports: Chemical Available (L) Port 1 400 Port 2 110 Port 3 100 The following amounts of Important Chemical A are required at your warehouses: Warehouse 1 Warehouse 2 Chemical Required (L) 380 230 The cost in£to ship 1L of chemical from each port to each warehouse is as follows: Warehouse 1 Warehouse 2 Port 1 £10 Port 2 £20 Port 3 £13 £45 £28 £11 (a) You want to know how to send these shipments as cheaply as possible. For- mulate this as a linear program (you do not need to formulate it in standard inequality form) indicating what each variable represents. (b) Suppose now that all is as in the previous question but that only 320L of Important Chemical A are now required at Warehouse 1. Any excess chemical can be transported to either Warehouse 1 or 2 for storage, in which case the company must pay only the relevant transportation…