Free Master of Data Science: Statistical Inference & Regression Models Questions and Answers

Question 1

Given that beliefs adhere to specific laws, which of the following best describes the probability calculus of beliefs?

Accepted Answer

Bayesian probability

Answer

Bayesian probability is a framework where probability is interpreted as a degree of belief or subjective confidence in an event. It provides a mathematical system for representing and updating these beliefs based on new evidence, adhering to specific laws of probability calculus. This approach contrasts with frequentist probability, which defines probability based on the long-run frequency of events.

Question 2

Identify the accurate statement.

Accepted Answer

Bayesian inference is the use of Bayesian probability representation of beliefs to perform inference

Answer

Bayesian inference is a statistical method that uses Bayes' theorem to update the probability for a hypothesis as more evidence or information becomes available. It fundamentally relies on the Bayesian interpretation of probability, where probabilities represent degrees of belief. This allows for a coherent framework to reason about uncertainty and make decisions based on updated beliefs.

Question 3

Which of the aforementioned is a random variable?

Accepted Answer

All of the above

Answer

A random variable is a variable whose value is a numerical outcome of a random phenomenon. The outcome of an exam (e.g., a score), the outcome of a coin flip (e.g., heads/tails mapped to 0/1), and the outcome of a die roll (e.g., numbers 1-6) are all examples where the result is uncertain and determined by chance. Therefore, all listed options qualify as random variables.

Question 4

Which one of the following random variables has a finite number of possible outcomes?

Accepted Answer

Discrete

Answer

A discrete random variable is one that can take on a finite or countably infinite number of distinct values. For instance, the number of heads in a series of coin flips or the outcome of a die roll are discrete. In contrast, a continuous random variable can take any value within a given range, having an uncountably infinite number of possible outcomes.

Question 5

The center of the distribution of a random variable is its anticipated value, or .

Accepted Answer

mean

Answer

The anticipated value, or expected value, of a random variable is its mean. It represents the long-run average value of the variable if the experiment were repeated many times. The mean serves as a central measure of the distribution, indicating where the values tend to cluster.

MS-DS Master of Data science Practice Test

MS-DS Master of Data science Practice Test

Free Master of Data Science: Statistical Inference & Regression Models Questions and Answers