Sove all questions KindlyjQuery22409209757406848311_1622504799029?AlphaTech, which is at the forefront of next generation communication chip for $10 million.

AlphaTech currently is in its final development stage of its flagship communication chip, SignalOne. The quality of the chip is measured by its latency level: Ultra-Low, Low and Medium. If the chip could achieve Ultra-Low latency, AlphaTech's valuation will increase to $100 million. If the chip could achieve Low or Medium, the AlphaTech's valuation will be $50 million and $20 million, respectively. There could also be a possibility that the chip would fail to achieve latency level and not viable to be commercialised. The followings are the probabilities for the eventual latency performance of SignalOne chip:

Ultra-Low ~ 0.10 Low ~ 0.20 Medium ~ 0.40 Not viable ~ 0.30

Alternatively, Evergreen Technology could acquire a 40% stake in AlphaTech at the initial phase for $6 million while it waits for the preliminary test report on a SignalOne prototype. The preliminary test report can be positive or negative, and the probability of each is 0.5. If the preliminary test report is positive, Evergreen Technology will then proceed to acquire the remaining 60% stake for $15 million. Given the positive preliminary test result, the probabilities for the eventual latency performance of SignalOne chip will be:

Ultra-Low ~ 0.25 Low ~ 0.35 Medium ~ 0.30 Not viable ~ 0.10

In the event that the preliminary test report is negative, Evergreen Technology will either sell off its 40% stake at $5 million or proceed to acquire the remaining 60% stake for $3 million. Given the preliminary test result is negative, the probabilities for the eventual latency performance of SignalOne chip will be:

Ultra-Low ~ 0.01 Low ~ 0.05 Medium ~ 0.20 Not viable ~ 0.74

(a) Examine the case presented above and show the decision tree with the relevant decision nodes, chance nodes, branches and payoff values correctly indicated.

(b) Solve the decision tree identified in Question 2(a) and discuss the decision to be made.

31. Consider the system of equations azcl + :62 = 1 and 351 + 112 = 2. (a) Show that the solution is $1: 1/(1 a) and 332 = 2 1/(1 a). (b) Set up and solve the system using the routine gauss that we wrote in class with a = 10\1 . Estimate fo ex dx by using the Midpoint Rule first with n = 2, and later with n = 25 rectangles. Use the following Maple commands: with( student ) to load the student package, middlesum( exp( x * x ), x - a .. b, n ) for the Midpoint sum, and evalf( %) to convert the sigma sum to a decimal number. For a help screen with examples, type: ? middlesum In Maple, the Gaussian function is typed: exp( * * *) Sketch the bell curve area and two midpoint rectangles either by hand or with the middlebox command. Then use the Maple command middlebox( exp( x * x ) , * = 0 ..2, 25 , color = blue-) to accurately plot 25 midpoint rectangles (your choice of color). 2. This is a follow-up problem to # 1. (a) The improper integral ex dx can be approximated by the proper integral fo ex dx from # 1. Use inequalities to find the maximum (worst-case scenario) error in this approximation by finding an upper bound for the "tail" integral S ex dx . Be as precise as possible and show step-by-step inequality work. (b) Use the Maple command int( exp( x42 ) , x = 2 .. infinity ) to find a symbolic answer for the improper integral. The output will be in terms of the error function "erf" from Statistics & Probability. Then type evalf( %) to obtain a highly-accurate decimal value for the integral. Compare with your upper bound in part (a). Which is larger, the actual value or the worst-case upper bound?1.) (20 points). The Gaussian function (x - 2) 2 P(x) - exp V2 ITS2 2s2 is very important in probability and statistics. Write a user-defined function (10 points) that takes as input the parameters x, u, and s and returns the value of the function evaluated for these parameters. You may use the Numpy function numpy . exp () to calculate the exponential. Then, write the programming commands (10 points) which call this function and plot it for x between -3 and 3 with u = 0 and s = 1 (for all values of x). Be sure to label your axes and show the plot