C++ program to calculate the fair price of the butterfly spread using path-dependent simulation and path-independent simulation of the stock prices. Using the following dynamics for the stock price and strike prices with the constant values: dSt = rStdt + x*StdWt S0 = 100 K1 = 95 K2 = 100 K3 = 105 r = 0:02 x = 0:05 T = 10

The register we discussed in class has two inputs, D and clock, and one output, Q. If you are interested, you can access a simulator of this circuit at http://www.falstad.com/circuit/e-edgedff.html (note that that simulator has an extra output, !Q, below Q). If D is 1 as clock transitions from 0 to 1, which of the following is true? A. Q is (or soon becomes) 0 B. Q is (or soon becomes) 1 C. Q oscillates between 0 and 1 D. Q holds a steady value, which could be 0 or 1

Write a Python program that implements the Taylor series expansion of the function (1+x) for any x in the interval (-1,1], as given by: 1(1+x) = x-x²/2 + x³/3 - x^/4 + x³/5. The program prompts the user to enter the number of terms n. If n> 0, the program prompts the user to enter the value of x. If the value of xis in the interval (-1, 1], the program calculates the approximation to l(1+x) using the first n terms of the above series. The program prints the approximate value. Note that the program should validate the user input for different values. If an invalid value is entered, the program should output an appropriate error messages and loops as long as the input is not valid. Sample program run: Enter number of terms: 0 Error: Zero or negative number of terms not accepted Enter the number of terms: 9000 Enter the value of x in the interval (-1, 1]: -2 Error: Invalid value for x Enter the value of x in the interval (-1, 1]: 0.5 The approximate value of ln (1+0.5000) up to 9000 terms…

Consider two traffic lights in a junction that each one has a 7-segment display to show the remaining time.  The traffic lights are working as follows: State1: Traffic light 1=GREEN     Traffic light 2=RED       for 10 seconds,State2: Traffic light 1=YELLOW     Traffic light 2=YELLOW       for 2 seconds,State3: Traffic light 1=RED     Traffic light 2=GREEN       for 6 seconds,GOTO State1 During each step, the amount of remaining time should be displayed on the 7-segment and it should be updated every one second. For example in State 1, the display shows 9, then after a second it shows 8, and ... finally, it shows 0 for one second, and the control moves to State 2Write an 8051 assembly program according to the Edsim51 configuration, LED 0, LED1 and LED 2 construct the first traffic light, and LED 3, LED 4, and LED 5 can be used for the 2nd traffic light. Assume that the lookup table for 7segment exists on memory at address 0F00h