SMUC Midterm Review

How many events do we expect in a Poisson interval to obtain the density function of an exponential distribution? 1 lambda 0 lambda*t

0

What is the total probability of a Uniform distribution? 1 0 Infinite 0.5

1

What is the output of this code: np.repeat(np.array([1,2,3,4]),2) 1 2 3 4 1 2 3 4 1 1 2 2 3 3 4 4 2 4 6 8 1 4 1 4

1 1 2 2 3 3 4 4

How can we get help on a particular function in Python? ?function_name ??function_name function_name(help) function_name(help.search)

?function_name

Drawing one pseudo-random uniform variable from the interval [0,1] for a coin toss experiment is... A Monte Carlo Simulation A Sawilowsky method A Monte Carlo Method A Simulation experiment

A Simulation experiment

What is a Dummy Dataset? A collection of simulated random variables A tidy dataset A dataset with nonsense data A really easy dataset

A collection of simulated random variables

What is a Monte Carlo simulation? A type of machine learning model that uses decision trees A computational algorithm that uses random numbers to simulate a wide range of possible outcomes for a particular system or process An optimization technique for finding the maximum or minimum value of a function A gambling technique used in casinos

A computational algorithm that uses random numbers to simulate a wide range of possible outcomes for a particular system or process

What is a resource in a DES? A function that generates a random number. A set of instructions to transform input data into output data. An object that flows through the simulation. A process that can be used by entities.

A process that can be used by entities.

What is Discrete Event Simulation (DES)? A technique to model continuous processes. A type of data analysis technique. A technique to model queuing problems. A technique to model statistical distributions.

A technique to model queuing problems.

What is an input variable in a Monte Carlo simulation? A variable that affects the behavior of the system or process being modeled An estimate of the population parameter being inferred A probability distribution used to generate random samples A random number generated by the simulation

A variable that affects the behavior of the system or process being modeled

What is the last step in developing a Monte Carlo simulation? Hide answer choices Define the problem that you want to solve Generate random numbers Aggregate the results Choose a probability distribution

Aggregate the results

Given a binomial distribution of two parameters, B(10; 0.5), choose the correct statement. The variable can take any value less than 10 Mean and variance are the same All are incorrect The expected value is 0.5

All are incorrect

Which of the following is NOT a characteristic of a Monte Carlo simulation? There are enough samples to ensure accurate results The algorithm used is valid for what is being modeled All the variables in the experiment are discrete The proper sampling technique is used

All the variables in the experiment are discrete

How do we call "n" in the example you can see below? def myf(n = 10): print(n) An optional argument A required argument A printeable parameter An adjustable parameter

An optional argument

What is a queue in a DES? A set of resources that can be used by entities. An ordered list of entities waiting for a process. A set of instructions for generating entities. A function that transforms data.

An ordered list of entities waiting for a process.

The concept we use to measure how two variables are linearly dependent on each other is called... Autocorrelation Correlation Independence Uniformity

Correlation

What is the first step to perform a monte carlo simulation? Replicate the simulation at least 1000 times Aggregate the simulation results Define the domain of the random variables to be simulated Simulating data using the sample() function

Define the domain of the random variables to be simulated

Which of the following is not a type of Simulation Direct Simulation Discrete-Events Simulation Stochastic Simulation Dynamic Simulation

Direct Simulation

How do we call a simulation characterized by sudden state changes over time Standard Simulation Discrete Events Simulation Monte Carlo Methods Monte Carlo Inference

Discrete Events Simulation

A system is a set of related... Entities or resources Attributes States Events

Entities or resources

Your objective is to simulate covid spread in the IE over 2021. What type of distribution is the most appropriate? Normal Exponential Geometric Poisson

Exponential

If we fix a good seed, the experiment will never be replicated. False True

False

What more rigorous method than a histogram can we use to see if the pseudo-random numbers have been generated uniformly? Hypothesis testing Bar plot Correlation plot Autocorrelation plot

Hypothesis testing

How should a set of variables be to be considered a simple random sample? Dependent and identically distributed Independent and with different distribution Independent and identically distributed Dependent and with different distribution

Independent and identically distributed

Choose the correct statement about the Poisson distribution: It can be approximated to a B(n;p) with n=100 and p=0.05 It measures the time elapsed until the next success Expected value and standard deviation match Measure the number of failures until the first success

It can be approximated to a B(n;p) with n=100 and p=0.05

For the random variable that represents the number of heads obtained by flipping a perfect coin 4 times, we find that Its expected value is 4 Its variance is 1 It follows a Poisson model Its expected value is 2 and its variance is 0.5

Its variance is 1

Which of the following can be simulated through a static model? Load capacity of a ship Wind speed Machine energy consumption People in a queue

Load capacity of a ship

Which of the following is a continuous system? Money available in an account Available ATMs Granted loans Number of followers in a fan page

Money available in an account

What are entities in a DES? Objects that flow through the simulation. Processes that transform the entities. Mathematical expressions that generate random numbers. Functions that transform input data into output data.

Objects that flow through the simulation.

X = Exponential r.v.; if s = 20 units of time has already passed without an event, what is the probability of t = 10? P(X>s+t) P(X>s) intersection P(X>t) P(X>s) P(X>t)

P(X>t)

Any Simulation Scientific Report should allow the Simulation to be... Replicated Shared Enjoyed Analysed

Replicated

In a DES, what type of processes do entities flow through? Sequential processes Random processes Continuous processes Stochastic processes

Sequential processes

In a system, the collection of variables necessary to describe it at any time point is called State List Attribute Event

State

In numpy we work with atomic vectors, what does this mean? That vectors can only store one type of data That the vectors are small in size That vectors share different types of data That the data type is preset for any vector

That vectors can only store one type of data

What is the main purpose of using Monte Carlo simulation for inference? To reduce the uncertainty about a statistical estimate Calculate the value of pi Perform bottleneck analysis To visualize simulated data

To reduce the uncertainty about a statistical estimate

If we want to generate random numbers from 1 to 6 to simulate a die we will use a... Normal Distribution Geometric Distribution Poisson Distribution Uniform Distribution

Uniform Distribution

An insurance company with 1000 clients has a probability of suffering an accident in one year = 0.005 We model the number of accidents in a year with a Binomial (1000; 0.005) We model the number of accidents in a year with a Normal (5; 2.23) We model the number of accidents in a year with a Chi-square We model the number of accidents in a year with a Poisson (λ=5)

We model the number of accidents in a year with a Binomial (1000; 0.005)

Simulation is an appropiate tool when... We want to perform a "what if..." analysis We want to do direct experimentation We want an actual disruption of the system All the options are correct

We want to perform a "what if..." analysis

What would be the result of adding the two following lists? a = [1,2,3] b = [4,5,6] a+b? [5,7,9] [[1,2,3],[4,5,6]] [1,2,3,4,5,6] 21

[1,2,3,4,5,6]

What function do we use to get some of the most important statistics that describe the info we have in a dataframe? df.summary() df.str() df.describe() df.info()

df.describe()

Given a Z standard normal distribution, specify the expected value and the standard deviation: We can not know mu = 0; sigma = 2 mu = 0; sigma = 1 mu = 1; sigma = 0

mu = 0; sigma = 1

What is the best function to simulate a categorical variable? np.random.choice() np.random.geometric() np.random.binom() np.random.shuffle()

np.random.choice()

Which function do we use to generate random numbers from a Gaussian distribution? np.random.nromgaus() np.random.gussian() np.random.normal() stats.normal.pdf()

np.random.normal()

What is the function used in R to generate equally probable pseudo-random numbers? np.random.uniform() np.random.seed() stats.uniforms() np.random()

np.random.uniform()

Which programming style are we using in SimPy? event-oriented process-oriented activity-oriented simulation-oriented

process-oriented

What function do we use to calculate the density of a specific number in a Uniform distribution? stats.uniform.pdf() stats.uniform.cdf() stats.uniform() stats.uniform.pmf()

stats.uniform.pdf()

What are the main properties of the pseudo random numbers? uniformity and randomness randomness and normality uniformity and independence normailty and independence

uniformity and independence

When do we say that a numerical sequence is statistically random? when they come from a continuous distribution when it contains no recognizable patterns or regularities when they come from a discrete distribution when the numbers are dependent

when it contains no recognizable patterns or regularities