Write a program to produce an array of integer random numbers. Your program should find out from the user how many numbers to store. It should then generate and store that many random integers (the random numbers must be between 1 and 999 inclusive). The program should then determine the smallest number, the largest number, and the average of all the numbers stored in the array. Finally, it should print out all the numbers on the screen, five numbers to a line with spaces in between. Once the contents of the array have been printed to screen, display the smallest number, largest number, and average determined previously. You should ensure that your program design in modular.

The Random class of Java library (java.util.Random) implements a random number generator. To generate random numbers, you construct an object of q the class Random, and then use the method nextInt(n) which returns a number between 0 (inclusive) and n (exclusive).

E.g.

import java.util.Random;

.....

Random generator = new Random();

.....

//generate a random number between 0 and 99 (inclusive)

int nextRand = generator.nextInt(100);

Alternatively use Math.random(), which returns a random value in the range 0.0 to 1.0 (then adjust to the correct range)

Portfolio Theory

1. What type of risk does a portfolio have with a beta of 1.5?

a. Systematic risk only. b. Unsystematic risk only. c. Systematic and unsystematic risk. d. Cannot determine from the question.

2. Which tools can help to determine an optimal investment portfolio?

1. Mean-variance optimization model. 2. Risk tolerance questionnaire. 3. Tactical asset allocation.

a. 1 only. b. 2 only. c. 1 and 2. d. All of the above.

3. The highest annual range of returns for the S&P 500 has occurred for which of the following?

a. 1-year rolling returns. b. 5-year rolling returns. c. 10-year rolling returns. d. 20-year rolling returns.

4. The _____ is a graphical representation of expected return and risk, as measured by beta.

a. ALA. b. CML. c. SML. d. Efficient frontier

5. Jocko was just told that the expected return for Echo stock was 20%, based on the CAPM. Assuming that the market return and the risk-free rate are 12% and 4%, respectively, what is the beta for Echo?

a. 1.0. b. 1.5. c. 2.0. d. 2.5.

Blitz Industries has a debt-equity ratio of 1.3. Its WACC is 8.5 percent, and its cost of debt is 6.2 percent. The corporate tax rate is 22 percent. a. What is the company’s cost of equity capital? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) b. What is the company’s unlevered cost of equity capital? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) c-1. What would the cost of equity be if the debt-equity ratio were 2? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) c-2. What would the cost of equity be if the debt-equity ratio were 1.0? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) c-3. What would the cost of equity be if the debt-equity ratio were zero? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Question 8.  A transmembrane protein uses a β barrel structure to span the cell membrane.  How can amino acid mutations in a protein within this β barrel structure affect interactions with the membrane and why? (Up to 50 words)  

Question 9.  Haemoglobin is a protein that carries oxygen in our red blood cells.  Sickle cell anaemia is a genetic disease in which Glu at position 6 of haemoglobin is mutated to a Val, rendering haemoglobin non-functional.

1. What type of amino acid change is this?  (1 mark)

2. Give one reason why this could affect the function of this protein.  (1 mark)

Question 10.  Lectin is a protein that binds carbohydrates and is critical for biological recognition processes in living organisms.  Describe what bonds and forces could be involved in lectin and carbohydrate interactions. (Up to 50 words)  

Question 11.  A hexokinase is an enzyme that adds a phosphate to glucose after it enters the cell, which is considered the first step of glycolysis.  One enzyme, hexokinase A (HKA), has a K_m of 0.02 mM, whereas another, hexokinase B (HKB), has a K_m of 1.0 mM.  Explain why some types of fast growing cancer cells would use HKA instead of HKB. (Up to 50 words)  

Create a java application that can solve the following differential equation and boundary condition with the Runge Kutta method and the secant method.

x' = f(t,x) = x + 0.09x² + cos(10*t) differential equation

x(0) + x(1) - 3.0 = 0            boundary condition

Starting with the initial guesses 0.7 and 1.0 for the (unknown) initial value, x(0), obtain an approximation to x(0) {for the final solution, x(t)} such that the boundary condition is satisfied to within a tolerance of 10^-4 . Use a fixed stepsize of 0.025 (i.e., take 40 steps each time you integrate the differential equation from t=0 to t=1). Write your program so that the output shows the values of x(0), x(1), and x(0)+x(1)-3 (the error in satisfying the boundary condition) at the end of each iteration of the secant method. After the last iteration of the secant method, re-integrate from t=0 to t=1 and print out the solution for x(t) over the range [0,1]. Your solution for x(t) should resemble the solution plotted below.

You approximation to x(0), when you finish, should be roughly 0.7378743818.

a) you can see a program for using bisection search to find the square root of x:

x = 25

epsilon = 0.01

low = 0.0

high = max(1.0, x)

guess = (low + high) / 2

numberofguesses = 1

while abs(guess ** 2 - x) > epsilon :

print('low =', low, 'high = ', high, 'guess = ', guess)

if guess** 2 > x : # the guess is too high, so move high down to guess

high = guess

else : # the guess is too low, so move low up to guess

low = guess

print('number of guesses:', numberofguesses)

print(guess, 'is close enough to the square root of ', x)

Try out the program, and fix any typos (mine or yours) so that it works. Think about why it starts high with max(1, x) in place of simply high = x. Change the program so that the value of x is read from the user. Ask the user for a positive number. If the user gives a negative number, then ask again, repeatedly until a positive number is given.

b) Modify the bisection search program shown above, so that it finds the cube root of a number. The number can be negative or positive.