Please help me solve the questions below.

In a particular two-state intensity-based model with constant transition intensities, the integrated generator matrix M = |A(u)dy has the form M = where b -b a =0.2(f-s) and b=0.1(1 -5). (i) Show that, in this case, M-= -(a+b)M . (ii) Hence deduce an explicit formula for e in terms of a and b. (iii) Ilence deduce a set of formulae for the transition probabilities p;(s,f).Jenny has a quadratic utility function of the form U(w) = w-10" w-. She has been offered a job with Company X, in which her salary would depend upon the success or otherwise of the company. If it is successful, which will be the case with probability % then her salary will be $40,000, whereas if it is unsuccessful she will receive $30,000. (i) Assuming that Jenny has no other wealth, state the salary range over which V(w) is an appropriate representation of her individual preferences. 121 (ii) Calculate the expected salary and the expected utility offered by the job. [2] (iii) Suppose she was also to be offered a fixed salary by Company Z. Determine the minimum level of fixed salary that she would accept to work for Company Z in preference to Company X. [3] (iv) Suppose that the owners of Company X are both risk-neutral and very keen that Jenny should join them and not Company Z. Determine whether the firm should agree to pay her a fixed wage, and, if so, how much. Comment briefly on your answer. [Total 8]