SIMULATION TECHNIQUES IN STATISTICS — DU B.Sc (hons) Statistics Previous Year Question Papers

(b) Generate 2 Poisson random variates with mean 2 using any suitable method. Use the following uniform random numbers: 0.3678, 0.7254, 0.1423, 0.8647, 0.5912. Show all steps clearly. (8,7) 7. (a) Given the following sequence of random numbers: Generate random variables with the following discrete probability distribution: Show all steps clearly using the inverse transform method. (b) Use simulation to estimate the value of the integral: Use the following random numbers: 0.15, 0.63, (i) The formula used for estimation (i) The final estimate (iii) Compare with the true value (8,7) Statistics (DSE) 2. There are TWO sections in this paper. (b) What is the difference between discrete and continuous simulation models? (c) Define Monte Carlo simulation and list two applications. (e) What is the purpose of statistical analysis of simulated data? (f) Define acceptance-rejection method and state its advantages. (5x3=15) 2. (a) Explain Linear Congruential Generator (LCG) method for generating pseudo-random numbers. What are the criteria for choosing good parameters? (b) Write the steps to generate random numbers using LCG with m = 8, a = 5, c = 1 and initial seed x, =3, in the usual notations. Generate first 5 3. (a) Explain how inverse transform method can be used to generate exponential random variables. (b) Using inverse transform method, generate 5 exponential random variates with mean 2 using the following random numbers: 4. (a) Explain the acceptance-rejection method for generating random variables. What are its key components? (b) Use acceptance-rejection method to generate normal random variables. Explain the steps. 5. (a) What is variance reduction in simulation? Explain the antithetic variates method with an example. (b) In a simulation study, how do you determine when to stop generating new data values? Explain with suitable criteria. (8,7) (a) Explain how to generate Poisson random variables. Write down the steps for the same.