15.2.66 One dimensional random variables and their characteristics
condition: The random variable \( x \) is specified by the distribution function \( F(x) \). Find the probability distribution density, mathematical expectation and variance of the random variable. \[ F(x)=\left\{\begin{array}{c} 0, x \leq 0 \\ \frac{x^{2}}{4}, 02 \end{array}\right. \]
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.