The population consisting of all married couples is collected. The data showing the age of 12 married couples is as follows:
| Husband’s age (years) | Wife’s age (years) | Husband’s age (years) | Wife’s age (years) |
| 32 | 27 | 51 | 50 |
| 25 | 30 | 48 | 46 |
| 36 | 34 | 37 | 36 |
| 72 | 65 | 50 | 42 |
| 37 | 37 | 51 | 46 |
| 36 | 38 | 36 | 35 |
i) Draw a scatter plot of the data
ii) Write two important characteristics of the data that emerge from the scatter plot.
iii) Fit a linear regression model to the data and interpret the result in terms of the comparative change in the age of husband and wife.
iv) Calculate the standard error of regression and the coefficient of determination for the data.
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Let G(t) be the amount of the glucose in the bloodstream of a patient at time t. Assume that the glucose is infused into the bloodstream at a constant rate of . At the same time, the glucose is converted and removed from the bloodstream at a rate proportional to the amount of the glucose present. If at
then
i) formulate the model.
ii) find g(t) at any time t.
iii) discuss the long term behavior of the model.
Which one of the following portfolios cannot lie on the efficient frontier as described by Markowitz?
| Portfolio | Expected return | Standard deviation |
| W | 10% | 25% |
| X | 5% | 7% |
| Y | 17% | 37% |
| Z | 12% | 13% |
A library wants to improve its service facilities in terms of the waiting time of its borrowers. The library has two counters at present and borrowers arrive according to Poisson distribution with arrival rate 2 every 10 minutes and service time follows exponential distribution with a mean of 15 minutes. The library has relaxed its membership rules and a substantial increase in the number of borrowers is expected. Find the number of additional counters to be provided if the arrival rate is expected to be twice the present value and the average waiting time of the borrower must be limited to half the present value.
A company manufacturing soft drinks is thinking of expanding its plant capacity so as to meet future demand. The monthly sale for the past 6 years are available. State, giving reasons, the type of modelling you will use to obtain good estimates for future demand so as to help the company make the right decisions. Also state four essentials and four non-essentials for the problem.
Ships arrive at a port at the rate of one in every 6 hours with exponential distribution of inter-arrival times. The time a ship occupies a berth for unloading has exponential distribution with an average of 12 hours. If the average delay of ships waiting for berths is to be kept below 15 hours, how many berths should be provided at the port?
Do the stability analysis of the following model formulated to study the effect of toxicant on prey-predator population and interpret the solution.
Where all the variables and constants are same as defined in the system (32)-(35) except for the following
Consider a discrete model given by
Investigate the linear stability about the positive steady state N by setting . Show that nt satisfies the equation
Hence show that is a bifurcation value and that as
the steady state bifurcates to a periodic solution of period 6.