Question 7 Which of the following autoregressive processes are stationary? In each case, identify the order. (a) z1 = 0.4z1-3+ Et (b) z4 = 0.7z–1 – 1.2z-2 + et (c) 4 = -0.2z-1 - 1.2z-3 +€
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- The price of a stock is modeled with a geometric Brownian motion with drift μ=-0.25 and volatility σ=0.4. The stock currently sells for $35. Assume that an option is available to purchase the stock in six months for $40. Find the expected payoff of the option.Make a program in matlab that graphs the solution of the partial differential equation with u(0,t) = 0, u(π,t) = 1, u(x,0) = 0. The program should graph the solution u(x,t). The program must request the evolution time.Test whether any of the functions given in options (i), (ii), and (or) (iii) is (are)the solution to the partial differential equation:
- 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.Consider the geometric Brownian motion with σ = 1: dS = μSdt + SdX, and consider the function F(S) = A + BSα. Find any necessary conditions on A, B, and α such that the function F(S) follows a stochastic process with no drift.Two very large tanks A and B are each partially filled with 100 gallons of brine. Initially, 100 pounds of salt is dissolved in the solution in tank A and 50 pounds of salt is dissolved in the solution in tank B. The system is closed in that the well-stirred liquid is pumped only between the tanks, as shown in Figure 3.3.7.(a) Use the information given in the figure to construct a mathematical model for the number of pounds of salt x1 (t) and x2(t) at time t in tanks A and B, respectively.(b) Find a relationship between the variables x1(t) and x2 (t) that holds at time t. Explain why this relationship makes intuitive sense. Use this relationship to help find the amount of salt in tank B at t = 30 min. FIGURE 3.3.7 Mixing tanks in Problem 9Chapter 3.3, Problem 9E, Two very large tanks A and B are each partially filled with 100 gallons of brine. Initially, 100
- EXAMPLE 3 Find the trajectories of the autonomous system (19) dxdt=y,dydt=x.The falling object in Example 2 satisfies the initial value problem dνdt=9.8−ν5,ν(0)=0.dνdt=9.8−ν5,ν(0)=0. a.Find the time that must elapse for the object to reach 98% of its limiting velocity. b.How far does the object fall in the time found in part a?Find the equilibrium solution for P. Furthermore determine whether P is initially increasing faster if the initial population is 120 or 200.
- Use J. David Logan Applied Partial Differential Equations Third Edition for section 2.3-2.7 and section 3.1-3.3 to make an equation cheat sheet Front and Back. I want it to be written, I need your help as soon as possibleTwo very large tanks A and B are partially filled with 100 gallons of brine each. Initially, 100 pounds of salt are dissolved in the solution in tank A and 50 pounds of salt are dissolved in the solution in tank B. The system is closed, since the well-mixed liquid is pumped only between the tanks as shown in the figure. 1. Use the information in the figure to construct a mathematical model for the number of pounds of salt x1(t) and x2(t) at time "t" in tanks A and B, respectively. 2. Find a relationship between the variables x1(t) and x2(t) that holds at time «t». 3. Explain why this relationship makes intuitive sense. 4. Use this relationship to help find the amount of salt in tank B at t = 30 min.Two interacting populations of hares and foxes can be modeled by the recursive equations h(t + 1) = 4h(t) − 2 f (t) f(t+1)=h(t)+ f(t). For each of the initial populations given in parts (a) through (c), find closed formulas for h(t) and f (t). a. h(0)= f(0)=100 b. h(0)=200, f(0)=100 c. h(0)=600, f(0)=500