ISYE 6644 MIDTERM EXAM /WITH 100% CORRECT
ANSWERS
Graphically, what is an indication that your pseudorandom number generator is "no
good" (M1L7). - CORRECT ANSWERS -Example was graphing two "random variates"
in the x-y plane that were generated from uniform distributions transformed into normal...
ISYE 6644 MIDTERM EXAM /WITH 100% CORRECT
ANSWERS
Graphically, what is an indication that your pseudorandom number generator is "no
good" (M1L7). - CORRECT ANSWERS -Example was graphing two "random variates"
in the x-y plane that were generated from uniform distributions transformed into normal
distr (Box Muller Method). If a pattern in the graph appears, this is "bad." You expect
lots of random points clustered around the center that spread out evenly in all directions
from the center. Spiral patterns = no good.
In Queuing models, what does each part of the Kendall notation mean: A/B/C (general
version) applied to a M/M/1 (a specific version)(M1L7)? - CORRECT ANSWERS -A =
Distrib of arrival times
B = Distrib. of service times
C = # of servers in the system
M = arrival times are Poisson process (lambda)
M = exponential service times (mu)
1 = a single server
"M" stands for Markov, but really it means exponential?
Describe what a "random walk" model is and what "motion" it converges to (M1L7)? -
CORRECT ANSWERS -Model where the variable "step" size changes randomly with
each time increment (step size = randomly sampled from a normal distribution?).
Converges to Brownian Motion: as time steps become smaller and # of steps larger.
Continuous time, stochastic.
Random samples from which distribution can be transformed into random variables of
any other distribution (M1L8)? - CORRECT ANSWERS -Uniform (0, 1)
What specific pseudorandom number generating algorithm was covered in detail in
Module 1? It involves choosing a seed value, two carefully chosen constants a and m,
using the modulus operator, and then normalizing all values to fit between 0 and 1 by
dividing by m (M1L8). - CORRECT ANSWERS -Linear Congruential Generator (LCG).
The Desert Island Generator is is an LCG with a=16807 and m = 2^31 - 1 (a very large
prime number.
X(i) = 16807X(i - 1) mod (2^31 - 1)
U(i) = X(i) / m
What are the 3 general steps for the inverse transform method (M1L8)? - CORRECT
ANSWERS -1. Generate the Unif (0, 1) PRN (U_i)
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