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% |
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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 |
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
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.
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.
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% |
Do the stability analysis of the following competing species system of equations with diffusion and advection
where V1 and V2 are advection velocities in x direction of the two populations with densities N1 and N2 respectively. a1 is the growth rate, b1 is the predation rate, d1 is the death rate, C1 is the conversion rate. D1 and D2 are diffusion coefficients. The initial and boundary conditions are:
at
and
where are the equilibrium solutions of the given system of equations.
Interpret the solution obtained and also write the limitations of the model.
A tumour is developing from the organ of a human body with concentration with growth and decay control parameters 7.2 and 2.7 respectively. In how many days the size of the tumor will be twice?