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\fProblem 4. Consider a combined birth and death process with initial population size no = 10, birth rate A = 0.5, and death rate # = 0.25. Determine the probability of extinction at time t.Consider a birth and death process with birth rates ); = (i + 1)2, i 2 0, and death rates u; = iu, i 2 0. (a) Determine the expected time to go from state 0 to state 4. (b) Determine the expected time to go from state 2 to state 5. (c) Determine the variances in parts (a) and (b).Consider the linear system of equations 5x1 -$1 + - T2 + 5x3 (a) Write down the components of the Jacobi iteration equation. Do not do any iterations, just write down the iteration mechanism. (b) With an initial guess x) = [1, 0, 0] apply, by hand, the Jacobi iteration until the approximate relative error falls below 0.7%.\fImplement Jacobi method using any programming language Implement Jacobi method using any programming language for using the following initial values 12x, + 3x,- 5x, = 1 x + 5x2 + 3x, = 28 3x + 7x + 13x3 = 76 X = 0 X