About this question
Hard · Market Microstructure · Quant Trader interview question · probability, power-law, market-microstructure, mean, variance
Empirical studies suggest that order sizes in equity markets approximately follow a power law, resembling a Zipf distribution. Suppose the probability that an order size, $X$, exceeds a certain value, $x$, is given by $P(X > x) \propto x^{-\alpha}$, where $\alpha \approx 1.5$. Based on this information, does this distribution have a finite mean? Does it have a finite variance?