What is the output of the following code segment?

int x = 5;

int y = x;

y++;

x--;

System.out.println(x+" "+y);

a) 6 4

b) 4 6

c) 5 6

What are the contents of the word2 and word3 after the following code executes?

String word2 = "Java"

String word3 = word2.toUpperCase();

a)word2 = JAVA,word3 = java

b) word2= Java, word3 = JAVA

c) word2 = Java, word3= Java

d) word2 = JAVA, word3 = JAVA

Consider the process of birth and death with three possible states (0, 1, and 2), whose respective probabilities steady state are P 0, P 1 and P 2. The birth and death rates are summarized in the following table: State birth rate death rate 0 4 0 1 2 4 2 0 6 a) Build the rate diagram of this birth and death process b) Develop the balance equations. c) Solve the equations to find P 0, P 1 and P 2 d) Use the general formulas of the birth and death process to calculate P 0, P 1 and P 2. Also calculate L and W.Problem 2: 15 points = [5 + 5 + 5] Consider a birth-and-death process, X - {X(t) : t 2 0}, with instant rates Xx = A and uk = / per hour. You are given information about the expected departure times from states 0 and 1 as follows. . E [So |X(0) = 0] = 1 hour . E[Si |X(0) = 1] = 12 minutes 1. Determine parameters A and / 2. Derive the limiting distribution, A = lim P[X(() - *] for any * 2 0 3. Find the limiting expectation, lim E[X(t)] SolutionWrite down the iterative schemes for the Jacobi, Gauss-Seidel and SOR methods. Explain how SOR is obtained from the Gauss-Seidel method. Explore convergence property of the Jacobi and SOR method for the system A,r = b 0 0 .. . 0 b = [1... 17 n = 30 0 2 Use r() = [000.. . Of , Wapt = 1+ sin Iterate until (x - z()| $ 0.00005 The exact solution a can be found as r = A\\b Implement the SOR method (.m file should be submitted). Jacobi and Gauss-Seidel can be found on the webpage (code Create a table k Error Jacobi Error SOR Ratio Jacobi (c) Ratio SOR (c) E. EsOR 10 K where E Janda 5law- error estimate for Jacobi, Egon - error estimate for SOR, K number of iterations which SOR method needed to reach the prescribed accuracy.Exercise Write down the iterative schemes for the Jacobi, Gauss-Seidel and SOR methods. Explain how SOR is obtained from the Gauss-Seidel method. Explore convergence property of the Jacobi and SOR method for the system Anr = b 2 -1 2 An = b = 1. . .1 n =30 0 0 2 Use x() = [000 . . . 0]' , Wopt = 1+ sin - Iterate until |r - x*)||