Explain, with examples, the difference between

Static and Dynamic Models,

Deterministic,and Stochastic Models.

Compare the risk of two securities 1 and 2 whose return distributions are given below:

<img src='./qimages/14778-1b.jpg'>

2. Consider the discrete time population model given by

Nt+1 for a population Nt,

where K is the carrying. capacity of the population, r is the intrinsic growth rate and b is a positive parameter. Determine the non-negative steady-state and discuss the linear stability of the model for 0 r 1. Also find the first bifurcation value of the parameter r.

3. Do the stability analysis of the following pre-predator model formulated to study the effect of toxicants on the competing species:

dN1/dt r1N1- a1N1N2 d1C0N1

dN2/dt r2N2 a2N1N2

dCo/dt k1p-g1Co-m1Co

dP/dt Q hP kPN1 gCoN1

under the conditions

N10, N20,

where Density of prey population,

Density of predator population,

Concentration of the toxicant in the individual of the prey population,

p Constant environmental toxicant concentration,

Q The exogenous rate of input of toxicant into the environment,

r1, a1, d1, r2, a2, k1, g1, m1, k and g are all positive constants.

4. A company has three factories F1, F2 and F3 that supply to three markets M1, M2 and M3. The transportation costs from each factory to each market are given in the table. Capacities ai's of the factories and market requirements bj's are shown below. Find the minimum transportation cost.

M1 M2 M3 ai
F1 2 1 3 20
F2 1 2 3 30
F3 2 1 2 10
bJ 10 10 20 40/60

Given a set of securities with portfolio values

wi's

Find a feasible set of portfolio of these securities.

Formulate the model for which the reproductive function of the cancer cells in the tumour surface is given by
c c 1/2 together with initial conditions c 20 x 10^5 at t 0. Also find the density of the cancer cells in the tumour's surface area at t =45 days.

What are residual plots and box plots? Give an example of each.

Let be the amount of the glucose in the bloodstream of a patient at time t. The glucose is infused into the bloodstream at a constant rate of k gm/min. At the same time, the glucose is converted and removed from the bloodstream at a rate proportional to the amount of glucose present. If the initial concentration of glucose in the bloodstream was Go, then find the concentration at any time t. Also find the limiting value of the concentration as t->oo.