15.2.63 One dimensional random variables and their characteristics
condition: Distribution density of the random variable \( f(x)=\frac{A}{1+x^{2}} \). Find: \( A, F(x), M[x] \), \( D[x], p\{0 \leq x \leq 1\} \), draw a graph \( f(x) \), \( F(x) \)
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.