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% |
According to Markowitz, a portfolio can lie on the efficient frontier only if no other portfolio offers a higher _______ ____ ________ ______ _________ _______ ________ _______ ________ ___ __________.
________ ______ _________ _____ ___ ___ ___.
________ _________ _______ _________ _______ ________ ____ ______.
_______ _________ ___ ________ ____ _______ ___ _______ ___ _______ ______ ____.
____ ____ ____ _________ ___ _____.
________ _____ ____ ____ __________ __________ __________.
_______ ________ ___ _______ ________ __________ ____ ____ _________ ________ ___.
____ ____ ___ ___ ______ _______ _________ ________ _________ ________ ________ ____.
___ __________ ______ ___ ____.
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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.
Companies considering the purchase of a computer must first assess their future needs in order to determine the proper equipment. A computer scientist collected data from seven similar company sites so that computer hardware requirements for inventory management could be developed. The data collected is as follows:
| Customer Orders (in thousands) | Add-delete items (in thousands) | CPU time (in hours) |
| 123.5 | 2.108 | 141.5 |
| 146.1 | 9.213 | 168.9 |
| 133.9 | 1.905 | 154.8 |
| 128.5 | 0.815 | 146.5 |
| 151.5 | 1.061 | 172.8 |
| 136.2 | 8.603 | 160.1 |
| 92.0 | 1.125 | 108.5 |
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.
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.
Return distributions of the two securities are given below:
| Return | Probabilities | |
| X | Y |
|
| 0.20 | 0.15 | 0.30 |
| 0.15 | 0.08 | 0.25 |
| 0.10 | 0.05 | 0.15 |
| 0.11 | 0.09 | 0.25 |
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 |
Let be a portfolio of two securities X and Y. Find the values of w1 and w2 in the following situations:
i) and P is risk free.
ii) and variance P is minimum.
iii) Variance P is minimum and and
.