a) A small number of observations dominate the total sum. b) The data is symmetric and bell-shaped. c) The probability of extreme values is negligible. d) The distribution always has a finite upper bound.
2. Which of the following functions best represents a power-law probability distribution?
a) P(x)∼e−λxP(x)∼e^{-λx} b) P(x)∼x−αP(x)∼x^{-α} c) P(x)∼12πσ2e−(x−μ)22σ2P(x)∼\frac{1}{2\pi\sigma^2} e^{-\frac{(x−μ)^2}{2\sigma^2}} d) P(x)=x+cP(x) = x + c
3. Why do normal distributions commonly appear in natural and social systems?
a) They result from the accumulation of small independent random variables. b) They always represent financial systems. c) They arise when data is generated from a single source. d) They only appear in symmetric datasets.
5. The degree distribution of the World Wide Web (WWW) follows a power-law. What does this imply?
a) A small number of websites (hubs) have extremely high connectivity, while most have very few links. b) All websites have approximately the same number of links. c) Websites are connected randomly without any preference for linking. d) The WWW graph follows a normal distribution.
6. In a power-law degree distribution of the web graph, what happens when a new page is created?
a) It is equally likely to link to any existing page. b) It has a higher probability of linking to a highly connected (popular) page. c) It is more likely to link to a randomly chosen low-degree page. d) It distributes links in a Gaussian manner.
7. How can you verify whether a dataset follows a power-law distribution?
a) Plot the frequency distribution on a log-log scale and check for a straight-line pattern. b) Compute the mean and standard deviation. c) Fit a normal distribution curve and check for symmetry. d) Apply the Central Limit Theorem.
9. The Barabási-Albert model generates networks that:
a) Follow a uniform degree distribution b) Are scale-free and exhibit power-law degree distribution c) Have equal probability of linking to any node d) Have constant node degrees over time
10. What happens when high-degree nodes are removed from a scale-free network compared to a random network?
a) A scale-free network collapses rapidly, while a random network degrades gradually. b) Both networks show similar behavior. c) A random network collapses faster. d) A scale-free network becomes more resilient.
