MS-DS Master of Data science Statistical and Probabilistic Analysis 4

Question 1

The Kolmogorov-Smirnov test is used to compare which of the following?

Accepted Answer

An empirical distribution to a reference distribution, or two empirical distributions

Answer

The KS test measures the maximum difference between cumulative distribution functions, used for goodness-of-fit or two-sample comparisons.

Question 2

If X ~ Binomial(n=10, p=0.5), what is Var(X)?

Accepted Answer

2.5

Answer

Variance of a Binomial is np(1-p) = 10 × 0.5 × 0.5 = 2.5.

Question 3

In multiple hypothesis testing, the Bonferroni correction adjusts the significance threshold by:

Accepted Answer

Dividing α by the number of tests

Answer

Bonferroni sets the per-test threshold to α/m (where m is the number of tests) to control the family-wise error rate.

Question 4

A researcher notices that residuals from a regression model increase in spread as fitted values increase. This pattern indicates:

Accepted Answer

Heteroscedasticity

Answer

Heteroscedasticity is non-constant variance in residuals, often visible as a fan shape in residual plots.

Question 5

The Central Limit Theorem guarantees that the sampling distribution of the mean approaches normality as n increases, regardless of population shape. Which condition is essential?

Accepted Answer

The samples must be independent and identically distributed with finite variance

Answer

CLT requires i.i.d. sampling and finite population variance; sample size of ~30 is often sufficient for most distributions.

MS-DS Master of Data science Practice Test

MS-DS Master of Data science Practice Test

MS-DS Master of Data science Statistical and Probabilistic Analysis 4