Question 1: With proper assumptions: (a) Develop the prey predator model for a community containing predators (species 1 and species 2) and prey (species 3). There is the completion for food among species 1 and 2 and also, within each predator species. [10] (b) Convert the developed equation into a SDE justifying all the proper sources of randomness in the system. [5] Question 2: Biomass is generated inside a bioreactor of volume V (m), as shown in the following diagram: 4: (m/s), Cr.in (mole/m), qs (m/s), Cs.in (mole/m) F+S Biomass (B) (-rp) = kg Cs 4F (m/s), CF (mole/m), 4: (m/s), C (mole/m) (a) Develop the set of equations with appropriate initial and/ boundary conditions to estimate the profile for concentration evaluation of feed F and S and that of biomass (B). [5] (b) Under steady state condition, convert the model equations developed in a set of non-linear equation of the form F(X) = 7. Also, provide the numerical technique to solve F(X) = 7. [2 +3] 10 ex e-*/2 Question 3: Generate 20 random numbers from the distribution and integrate 211 dx 211 [3+2]