Determine the state transition matrix A. Explain your reason.

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

A pandemic infection is spreading in a population and it is killing 5% of sick people in a month. The rest of sick people

are recovering as of the end of the month. According to statistics, each sick person infects 2 well people in each month.

Unfortunately, there is no any evidence to say that the people, who are recovered will develop an immune response.

Answer the following questions according to information given.

a. Determine the state transition matrix A. Explain your reason. (5 pts)

b. Find the characteristic equation. (10 pts)

Calculate the eigen values and eigen vectors for the process. (10 pts)

d. Propose an initial condition to reach the stady state in the shortest duration. (15 pts)

e. Assume all the population are well initially, determine the number of death people at 10th month? (15 pts)

 

The monthly profit of a company is decreasing due to the Covid-19 pandemi (Figure-1). An estimation of the profit for the

next month is required in order to decide some investments. a) use linear (Cx+D) estimation and determine the next

month's profit expectation. b) use a second order function (Cx²+Dx+E) to estimate the next month's profit expectation.c)

Which estimation is better? Show the better one by showing the total error is lower.

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