ISYE 6644 COMPREHENSIVE QUESTIONS AND
ANSWERS SET A+
✔✔Suppose that you are testing 100 observations to see if they are exponential (with
unknown rate parameter λ). You decide to break the hypothesized p.d.f. into 5 intervals.
How many degrees of freedom will your resulting chi-square goodness-of-fit test statistic
have? - ✔✔The degrees of freedom is k−1−s=5−1−1=3
✔✔TRUE or FALSE? The Weibull distribution is a special case of the exponential
distribution - ✔✔FALSE. (It's the other way around!)
✔✔TRUE or FALSE? A search algorithm such as bisection or Newton is required to
obtain the MLEs for the two Weibull parameters. - ✔✔TRUE (the r parameter of the
Weibull distribution cannot be determined in closed form).
✔✔goodness-of-fit tests - ✔✔Kolmogorov-Smirnov
Cramer-von Mises
Anderson-Darling
Shapiro-Wilk
✔✔Which of the following problematic issues can arise in input data analysis? - ✔✔Not
enough data
Data coming from strange-looking, "non-standard" distributions
Nonstationary data (in which the distribution appears to change over time)
Correlated data
✔✔TRUE or FALSE? Arena has an Input Analyzer that automates distribution fitting for
certain well-known distributions. - ✔✔TRUE. (It's often a great time-saver!
✔✔Suppose that a machine consists of components A, B, and C. If any of the
components fail, then the machine breaks down. The failure times for A, B, and C are
exponential (with probability 0.5), normal (w.p. 0.1), and Weibull (w.p. 0.4), respectively.
, YES or NO? Would the composition method be a good choice to generate the overall
machine breakdown time for this scenario? - ✔✔YES. Composition would be much
more efficient than generating all three failure times for A, B, and C, and then taking the
minimum.
✔✔Let H and W denote a person's height and weight. Which of the following best
describes the joint distribution of ( H , W )? - ✔✔Bivariate normal distribution with
positive correlation coefficient
✔✔The multivariate normal distribution's covariance matrix ∑ can be decomposed into
the form ∑ = C C T. What does the C informally stand for? - ✔✔Cholesky
✔✔TRUE or FALSE? The times between Poisson( λ ) arrivals are i.i.d. Exp( λ ). -
✔✔TRUE. (... as long as ( λ ) doesn't change over time.)
✔✔TRUE or FALSE? The times between nonhomogeneous Poisson( λ ) arrivals are
i.i.d. Exp( λ ). - ✔✔FALSE. (They're independent, but the distribution changes as the
arrival rate λ ( t ) changes over time.)
✔✔What is the recommended method to generate nonhomogeneous Poisson arrivals?
- ✔✔Thinning
✔✔Consider the time series Y i = ϕ Y i − 1 + ϵ i , i = 1 , 2 , ..., where the ϵ i's are i.i.d.
normal. What is this time series called? (Give the best answer.) - ✔✔first-order
autoregressive process
✔✔Consider the waiting time W i Q of the i th customer in an M / M / 1 queuing system
with first-in-first-out services. What relation allows you to calculate customer ( i + 1 )'s
waiting time W i + 1 Q based on W i Q, customer i's service time S i, and customer ( i +
1 )'s interarrival time I i + 1? - ✔✔Lindley's equation
W^Q_{i+1} = max\{0, W^Q_i + S_i - I_{i+1}\}
✔✔Brownian motion is also known as ... - ✔✔Wiener process
✔✔Let W ( t ) denote a Brownian motion process at time t. What is C o v ( W ( 2 ) , W (
3 ) )? - ✔✔min(s, t)
2
✔✔TRUE or FALSE? Unif(0,1) pseudo-random numbers can be used to generate pretty
much any other random variates, e.g., exponential, normal, and Poisson. - ✔✔TRUE.
That's the point of this module!
ANSWERS SET A+
✔✔Suppose that you are testing 100 observations to see if they are exponential (with
unknown rate parameter λ). You decide to break the hypothesized p.d.f. into 5 intervals.
How many degrees of freedom will your resulting chi-square goodness-of-fit test statistic
have? - ✔✔The degrees of freedom is k−1−s=5−1−1=3
✔✔TRUE or FALSE? The Weibull distribution is a special case of the exponential
distribution - ✔✔FALSE. (It's the other way around!)
✔✔TRUE or FALSE? A search algorithm such as bisection or Newton is required to
obtain the MLEs for the two Weibull parameters. - ✔✔TRUE (the r parameter of the
Weibull distribution cannot be determined in closed form).
✔✔goodness-of-fit tests - ✔✔Kolmogorov-Smirnov
Cramer-von Mises
Anderson-Darling
Shapiro-Wilk
✔✔Which of the following problematic issues can arise in input data analysis? - ✔✔Not
enough data
Data coming from strange-looking, "non-standard" distributions
Nonstationary data (in which the distribution appears to change over time)
Correlated data
✔✔TRUE or FALSE? Arena has an Input Analyzer that automates distribution fitting for
certain well-known distributions. - ✔✔TRUE. (It's often a great time-saver!
✔✔Suppose that a machine consists of components A, B, and C. If any of the
components fail, then the machine breaks down. The failure times for A, B, and C are
exponential (with probability 0.5), normal (w.p. 0.1), and Weibull (w.p. 0.4), respectively.
, YES or NO? Would the composition method be a good choice to generate the overall
machine breakdown time for this scenario? - ✔✔YES. Composition would be much
more efficient than generating all three failure times for A, B, and C, and then taking the
minimum.
✔✔Let H and W denote a person's height and weight. Which of the following best
describes the joint distribution of ( H , W )? - ✔✔Bivariate normal distribution with
positive correlation coefficient
✔✔The multivariate normal distribution's covariance matrix ∑ can be decomposed into
the form ∑ = C C T. What does the C informally stand for? - ✔✔Cholesky
✔✔TRUE or FALSE? The times between Poisson( λ ) arrivals are i.i.d. Exp( λ ). -
✔✔TRUE. (... as long as ( λ ) doesn't change over time.)
✔✔TRUE or FALSE? The times between nonhomogeneous Poisson( λ ) arrivals are
i.i.d. Exp( λ ). - ✔✔FALSE. (They're independent, but the distribution changes as the
arrival rate λ ( t ) changes over time.)
✔✔What is the recommended method to generate nonhomogeneous Poisson arrivals?
- ✔✔Thinning
✔✔Consider the time series Y i = ϕ Y i − 1 + ϵ i , i = 1 , 2 , ..., where the ϵ i's are i.i.d.
normal. What is this time series called? (Give the best answer.) - ✔✔first-order
autoregressive process
✔✔Consider the waiting time W i Q of the i th customer in an M / M / 1 queuing system
with first-in-first-out services. What relation allows you to calculate customer ( i + 1 )'s
waiting time W i + 1 Q based on W i Q, customer i's service time S i, and customer ( i +
1 )'s interarrival time I i + 1? - ✔✔Lindley's equation
W^Q_{i+1} = max\{0, W^Q_i + S_i - I_{i+1}\}
✔✔Brownian motion is also known as ... - ✔✔Wiener process
✔✔Let W ( t ) denote a Brownian motion process at time t. What is C o v ( W ( 2 ) , W (
3 ) )? - ✔✔min(s, t)
2
✔✔TRUE or FALSE? Unif(0,1) pseudo-random numbers can be used to generate pretty
much any other random variates, e.g., exponential, normal, and Poisson. - ✔✔TRUE.
That's the point of this module!
