15.2.60 One Dimensional Random Variables and Their Characteristics
Condition: random values \ (\ quad x_ {k}, k = 1.2, \ ldots, n \), distributed evenly on the segment \ ([0, a] \). Find the function of the distribution and the function of the probability density of the random value \ (y = \ max _ {1 \ leq k \ leq n} \ left \ {x_ {1}, x_ {2}, \ ldots, x_ {n} \ right \} \), considering the magnitude \ (x_ {k} \) Independent. Calculate the mathematical expectation and dispersion of a random value \ (y \). Calculate the probability \ (p (y \ geq a / 2) \). \ (A = 10, n = 3 \).
Study of Discrete and Continous One-Dimensional Random Variaans, Calculation of Their Characteristics Such as Mathematical Expectation, Standard Deviation, Standard Deviation, Moments, Distribution and Density Functions. WE ALSO Consider Problems on Known Distributions - Gauss, Bernoulli, Poisson. Finding The Probabilites of Various Events, Including Those from Evedey Life.