MS-DS Master of Data science FREE MS-DS Master of Data science Statistical and Probabilistic Analysis Questions and Answers 2

Question 1

In Bayesian inference, what does the posterior distribution represent?

Accepted Answer

The updated belief about a parameter after observing data

Answer

The posterior distribution combines the prior belief with the likelihood of observed data using Bayes' theorem to produce an updated belief about the parameter.

Question 2

Which property must a valid covariance matrix satisfy?

Accepted Answer

It must be positive semi-definite

Answer

A valid covariance matrix must be symmetric and positive semi-definite, ensuring all variances and linear combinations of variables have non-negative variance.

Question 3

What does the Kolmogorov-Smirnov test primarily assess?

Accepted Answer

Whether a sample follows a specified distribution

Answer

The Kolmogorov-Smirnov test compares the empirical distribution function of a sample against a reference cumulative distribution function to assess goodness of fit.

Question 4

If X and Y are independent random variables, what is Var(X - Y)?

Accepted Answer

Var(X) + Var(Y)

Answer

For independent random variables, the variance of their difference equals the sum of their individual variances because independence means the covariance term is zero.

Question 5

In maximum likelihood estimation, what is the Fisher information used to approximate?

Accepted Answer

The variance of the MLE asymptotically

Answer

The inverse of the Fisher information provides the asymptotic variance of the MLE, forming the basis of the Cramér-Rao lower bound.

MS-DS Master of Data science Practice Test

MS-DS Master of Data science Practice Test

MS-DS Master of Data science FREE MS-DS Master of Data science Statistical and Probabilistic Analysis Questions and Answers 2