15.2.53 One dimensional random variables and their characteristics
Condition: The base of the triangle is the segment from the point \(A\) to the point \(C\). The third vertex \( B(x, y) \) is located in the region D. Considering all positions of the point \( B \) in the region \( D \) to be equally possible, find the mathematical expectation of the area of the triangle \( A B C \). \[ A(0 ; 0), C(19 ; 0), D=\left\{0 \leq x \leq 19 ; 0 \leq y \leq x^{2}\right\} \]
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.