15.2.67 One dimensional random variables and their characteristics
condition: The mathematical expectation \( a \) and the standard deviation \( \sigma \) of a normally distributed random variable are known. Find the probability of this value falling into the given interval \( (\alpha ; \beta) \). \[ a=4, \sigma=5, \alpha=2, \beta=11 \]
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.