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 likelihood of data given the parameter

Answer

The initial assumption before any data is collected

Answer

The sampling distribution of a test statistic

Question 2

Which property must a valid covariance matrix satisfy?

Accepted Answer

It must be positive semi-definite

Answer

All diagonal entries must be zero

Answer

It must have a determinant of exactly one

Answer

All off-diagonal entries must be positive

Question 3

What does the Kolmogorov-Smirnov test primarily assess?

Accepted Answer

Whether a sample follows a specified distribution

Answer

Whether two population means are equal

Answer

Whether variances across groups are homogeneous

Answer

Whether residuals are autocorrelated

Question 4

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

Accepted Answer

Var(X) + Var(Y)

Answer

Var(X) - Var(Y)

Answer

Var(X) × Var(Y)

Answer

Var(X) / Var(Y)

Question 5

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

Accepted Answer

The variance of the MLE asymptotically

Answer

The bias of the estimator

Answer

The posterior probability of the parameter

Answer

The p-value of a hypothesis test

Question 6

Which distribution arises as the sum of squared independent standard normal random variables?

Accepted Answer

Chi-squared distribution

Answer

F-distribution

Answer

Student's t-distribution

Answer

Exponential distribution