15.2.54 One dimensional random variables and their characteristics
Condition: Two vertices of the triangle coincide with the points \( A(0 ; 0) \) and \( C(19 ; 0) \). The position of the third vertex \( B(x ; y) \) is equally possible at any point in the region \( D=\{0 \leq x \leq 19 \); \( \left.0 \leq y \leq(x-19)^{2}\right\} \). Find the probability density function for the area of the triangle and the expected value of this area.
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.