MS-DS Master of Data science FREE MS-DS Master of Data science Statistical and Probabilistic Analysis Questions and Answers 3

Question 1

What does the Markov chain Monte Carlo (MCMC) method primarily accomplish in statistical analysis?

Accepted Answer

It samples from complex posterior distributions that are difficult to compute analytically

Answer

It finds the exact maximum of the likelihood function

Answer

It eliminates the need for prior distributions in Bayesian analysis

Answer

It calculates exact p-values for nonparametric tests

Question 2

In the context of hypothesis testing, what does statistical power represent?

Accepted Answer

The probability of correctly rejecting H₀ when H₁ is true

Answer

The probability of rejecting H₀ when H₀ is true

Answer

The probability of failing to reject H₀ when H₁ is true

Answer

The probability of the observed data under H₀

Question 3

Which condition is required for the Gauss-Markov theorem to guarantee that OLS estimators are BLUE?

Accepted Answer

Errors must have constant variance and zero mean with no autocorrelation

Answer

Errors must follow a normal distribution

Answer

The dependent variable must be binary

Answer

The sample size must exceed 30

Question 4

What is the primary purpose of the Expectation-Maximization (EM) algorithm?

Accepted Answer

To find maximum likelihood estimates when data has missing or latent variables

Answer

To perform dimensionality reduction on high-dimensional data

Answer

To compute Bayesian credible intervals for regression coefficients

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To test for stationarity in time series data

Question 5

For a multivariate normal distribution, what does a zero covariance between two variables imply?

Accepted Answer

The variables are both uncorrelated and independent

Answer

The variables are uncorrelated but may still be dependent

Answer

The variables have identical marginal distributions

Answer

The conditional distribution is uniform

Question 6

What does the Akaike Information Criterion (AIC) balance when comparing statistical models?

Accepted Answer

Goodness of fit and model complexity

Answer

Bias and variance of predictions

Answer

Type I and Type II error rates

Answer

Prior probability and posterior probability