Statistical and Probabilistic Analysis Flashcards
7 cards from real MS-DS Master of Data science practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
Read the first 7 Statistical and Probabilistic Analysis flashcards as text
The Kolmogorov-Smirnov test is used to compare which of the following?
Answer: An empirical distribution to a reference distribution, or two empirical distributions
The KS test measures the maximum difference between cumulative distribution functions, used for goodness-of-fit or two-sample comparisons.
If X ~ Binomial(n=10, p=0.5), what is Var(X)?
Answer: 2.5
Variance of a Binomial is np(1-p) = 10 × 0.5 × 0.5 = 2.5.
In multiple hypothesis testing, the Bonferroni correction adjusts the significance threshold by:
Answer: Dividing α by the number of tests
Bonferroni sets the per-test threshold to α/m (where m is the number of tests) to control the family-wise error rate.
A researcher notices that residuals from a regression model increase in spread as fitted values increase. This pattern indicates:
Answer: Heteroscedasticity
Heteroscedasticity is non-constant variance in residuals, often visible as a fan shape in residual plots.
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?
Answer: The samples must be independent and identically distributed with finite variance
CLT requires i.i.d. sampling and finite population variance; sample size of ~30 is often sufficient for most distributions.
Maximum Likelihood Estimation (MLE) selects parameters that:
Answer: Maximize the probability of observing the given sample under the assumed model
MLE finds parameters θ that maximize L(θ|data), the likelihood of the observed data under the parametric model.
Given two events A and B where P(A) = 0.5 and P(B|A) = 0.4, what is P(A ∩ B)?
Answer: 0.2
By the multiplication rule, P(A ∩ B) = P(B|A) × P(A) = 0.4 × 0.5 = 0.2.