Question:

You are buying a house in Fall Creek. The neighborhood is susceptible to flooding as a result of intense summer thunderstorms and ice jams. During the decade you plan to live in the house, you know there is a chance that a 100-year flood will occur and some chance that a 500-year flood will occur. If a 100-year flood occurs, the damages to the house will be "moderate" ($30,000) with 90% probability and "severe" ($50,000) with 10% probability. If a 500-year flood occurs, the damages to the house will be "moderate" with 70% probability and "severe" with 30% probability. Any other flooding event of smaller magnitude can be assumed to have no damages. The probability of having more than one flood during the period can also be neglected. You can take one of three actions: (1) do not get flood protection (2) install foundation vents, at a cost of $5,000, so that it can protect against moderate impacts, or (3) spend $15,000 and design the house to protect against any severe impacts.

Show that the probability that at least one 100-year flood and at least one 500-yearflood will occur in a decade are approximately 9.6% and 2% respectively. (Hint: a 100-year flood is a flood event that has a 1 in 100 chance (or 1%)of being equaled or exceeded any given year)

Draw a decision tree for this problem. Fully label all branches, nodes, and outcomes with the given information.

Calculate the expected value at each node. If money is the only concern, what should your decision be?

How does the idea of making this decision solely on expected value make you feel? Would you feel comfortable making this real-world decision using a decision tree? Explain why or why not.

E. After discussing with your partner, you decide to install foundation vents and protect your house against moderate impacts. You move in the house and receive a letter from the city proposing a new plan for the residents of Fall Creek to raise the protection in Cascadilla Creek, effectively reducing the impacts of a 500-year flood

6.7 (Reachability matrix for reachable canonical form) Consider a system in reach- able canonical form. Show that the inverse of the reachability matrix is given by al a2 an 0 1 a1 . . an-1 = 0 0 1 . . a1 0 0 0 . . . 6.7 (Reachability matrix for reachable canonical form) Consider a system in reach- able canonical form. Show that the inverse of the reachability matrix is given by a a2 an 0 1 a1 . . an-1 W = 0 0 1 . . a1 0 0 0 . . .Problem 1: For the following transfer function s2 + 2s + 3 G(S)= $3 + 5s2 + 8s + 4 a. Obtain the state space representation in controllable canonical form. b. Obtain the state space representation in observable canonical form. c. Repeat parts a & b using MATLAB. Problem 2: Given the following transfer function s+9 G(S) = $2 + 3s + 2 Find the state space representation and draw a block diagram for the system in the following forms a) Controllable Canonical Form. b) Observable Canonical Form. c) Diagonal Canonical Form. Repeat a and b using MATLAB.Which one of the following is correct regarding the Pearson product-moment correlation and serial correlations regarding the value of a variable? Multiple Choice O For the Pearson product-moment correlation, the value would be in the range of -1 to +1, but when positive serial correlation exists the Durbin-Watson statistic approaches 1. O For the Pearson product-moment correlation, the value would be in the range of -1 to +1, but when positive serial correlation exists the Durbin-Watson statistic approaches 0. O For the Pearson product-moment correlation, the value would be in the range of 0 to 1, but when positive serial correlation exists the Durbin Watson statistic approaches -1. O For the Pearson product-moment correlation, the value would be in the range of 0 to 1, but when positive serial correlation exists the Durbin Watson statistic approaches 10(5) 55+3 W3) (5 +l)(s+2)(s+3) Find a} A state space representation of diagonal canonical form. b} A state space representation of controllable canonical form. c} A state space representation of observable canonical form