15.2.59 One dimensional random variables and their characteristics
Condition: The random variable \( X \) has a Pareto distribution with probability density \( f(x)=\frac{a}{x_{0}}\left(\frac{x_{0}}{x}\right)^{a+1} \), with \( x_{0} \leq x \) and \( f(x)=0 \) for \( x0\right. \) and \( \left.x_{0}>0\right) \) Find: \( M(x), \quad P\left(x_{0} \leq x
Study of discrete and continuous one-dimensional random variables, calculation of their characteristics such as mathematical expectation, variance, standard deviation, moments, distribution and density functions. We also consider problems on known distributions - Gauss, Bernoulli, Poisson. Finding the probabilities of various events, including those from everyday life.