15.2.55 One dimensional random variables and their characteristics
Condition: One vertex of the triangle is at the point \( A(0; 0)\), the second is at the point \( B(19; 0)\), and the position of the third vertex is equally possible in the area bounded by the lines \( y=0, x=19 \) and \( y=\sqrt{19 x} \). Find the probability density function for the area of the triangle, the mathematical expectation of this area and its variance.
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.