Stochastic Models Quiz: Test Your Knowledge of Applications in Finance, Insurance, and Queuing

Question 1

A call center receives an average of 5 calls per minute. Assuming calls arrive independently, which probability distribution best models the number of calls received in a 10-minute interval?

Accepted Answer

Poisson distribution

Answer

Normal distribution

Answer

Binomial distribution

Answer

Exponential distribution

Question 2

An insurance company uses a stochastic model to determine car insurance premiums. What key factor does the model likely incorporate to assess risk and calculate premiums?

Accepted Answer

Probability of accidents

Answer

Driver's favorite music

Answer

Car color

Answer

Average speed limit on local roads

Question 3

A stock price follows a geometric Brownian motion. Which of the following statements is TRUE about the future price of the stock?

Accepted Answer

The logarithm of the future price is normally distributed.

Answer

The future price is predictable with certainty.

Answer

The future price is uniformly distributed.

Question 4

Which stochastic process is commonly used to model the random movement of a particle suspended in a fluid?

Accepted Answer

Brownian motion

Answer

Poisson process

Answer

Markov chain

Answer

Bernoulli process

Question 5

In a queuing system, the arrival rate is 4 customers per minute and the service rate is 6 customers per minute. What is the traffic intensity (ρ) of this system?

Accepted Answer

0.67

Answer

2.4

Answer

1.5

Answer

0.4

Question 6

A Markov chain is used to model the weather with states: sunny, cloudy, and rainy. If it is sunny today, the probability of it being rainy tomorrow is 0.1. What does this probability represent in the context of the Markov chain?

Accepted Answer

Transition probability

Answer

Initial probability

Answer

Steady-state probability

Answer

Absorbing probability

Question 7

A Monte Carlo simulation is used to estimate the price of a complex financial derivative. Which of the following is NOT a characteristic of the Monte Carlo method?

Accepted Answer

Provides an exact analytical solution

Answer

Can handle complex and high-dimensional problems

Answer

Relies on repeated random sampling

Answer

Approximates the solution through simulation

Question 8

In the context of inventory management, what does the newsvendor model aim to determine?

Accepted Answer

Optimal order quantity to minimize expected cost

Answer

Optimal selling price to maximize revenue

Answer

Optimal storage capacity for inventory

Answer

Optimal delivery schedule for suppliers

Question 9

A website experiences random traffic throughout the day. Which stochastic process can be used to model the number of visitors to the website over time?

Accepted Answer

Poisson process

Answer

Geometric Brownian motion

Answer

Markov chain

Answer

Random walk