Can you help me with f and g?What they are asking is, what do you shade in? Not the power set. At least for F

Q3 3 Points 1 0 2 4 0 6 01 5 - -1 0 10 00 0 0 1 1 The reduced row echelon form of the augmented matrix of a linear system is given above. Describe the solution set of this linear system in parametric vector form. Please select file(s) Select file(s) Save Answer

3. Suppose you have 12 professors in a department and you have to chose members of departmental committees. (a) How many ways can you pick members for one 4 people committee? (b) How many ways can you pick members for two different 4 people committees if no-one can serve on both committees? (c) How many ways can you pick members for two different 4 people committees if people can serve on both committees? (d) How about if you need members for a 4 person, a 5 person, and a 3 person committee, people cannot serve on more than one committee? (e) How about if you need members for a 4 person, a 5 person, and a 3 person committee, people can serve on more than one committee? (f) How about if you need members for a 4 person, a 5 person, and a 3 person committee, people cannot serve on more than one committee, and the first person chosen for each committee serves as chair?

Q4 3 Points 1 Let A = 2 3 7 5 11 Give one nontrivial solution X of the homogeneous system Ax = 0. (Your vector x should have explicit numbers as its entries, as opposed to variables/parameters). Show your work for how you found it. Please select file(s) Select file(s) Save Answer

4. Assume that a risk-free money market account is added to the market described in Q3. The continuously compounded rate of return on the money market account is log (1.1). (i) For each given μ, use Lagrange multipliers to determine the proportions (as a function of μ) of wealth invested in the three assets available for the minimum variance portfolio with expected return μ. (ii) Determine the market portfolio in this market and calculate its Sharp ratio.

3. A market consists of two risky assets with rates of return R₁ and R2 and no risk-free asset. From market data the following have been estimated: ER₁ = 0.25, ER2 = 0.05, Var R₁ = 0.01, Var R2 = 0.04 and the correlation between R1 and R2 is p = -0.75. (i) Given that an investor is targeting a total expected return of μ = 0.2. What portfolio weights should they choose to meet this goal with minimum portfolio variance? Correct all your calculations up to 4 decimal points. (ii) Determine the global minimum-variance portfolio and the expected return and variance of return of this portfolio (4 d.p.). (iii) Sketch the minimum-variance frontier in the μ-σ² plane and indicate the efficient frontier. (iv) Without further calculation, explain how the minimum variance of the investor's portfolio return will change if the two risky assets were independent.

2. A landlord is about to write a rental contract for a tenant which lasts T months. The landlord first decides the length T > 0 (need not be an integer) of the contract, the tenant then signs it and pays an initial handling fee of £100 before moving in. The landlord collects the total amount of rent erT at the end of the contract at a continuously compounded rate r> 0, but the contract stipulates that the tenant may leave before T, in which case the landlord only collects the total rent up until the tenant's departure time 7. Assume that 7 is exponentially distributed with rate > 0, λ‡r. (i) Calculate the expected total payment EW the landlord will receive in terms of T. (ii) Assume that the landlord has logarithmic utility U(w) = log(w - 100) and decides that the rental rate r should depend on the contract length T by r(T) = λ √T 1 For each given λ, what T (as a function of X) should the landlord choose so as to maximise their expected utility? Justify your answer. Hint. It might be…

Please ensure that all parts of the question are answered thoroughly and clearly. Include a diagram to help explain answers. Make sure the explanation is easy to follow. Would appreciate work done written on paper. Thank you.

Consider the proof below: Proposition: If m is an even integer, then 5m +4 is an even integer. Proof: We see that |5m+4=10n+4 = 2(5n+2). Therefore, 5m+4 is an even integer. **Note: you may assume the proof is valid, just poorly written. Based upon the Section 1.3 screencast and the reading assignment, select all writing guidelines that are missing in the proof. Proof begins by stating assumptions ✓ Proof has an invitational tone/uses collective pronouns Proof is written in complete sentences Each step is justified ☐ Proof has a clear conclusion