15.2.28 One dimensional random variables and their characteristics

Problem: It's known that the continuous random variable \( \xi \) is distributed in accordance with the normal law of distribution with the parameters \( m=-1 \) and \( \sigma=4 \). 1. Find the laws of distribution in the form of distribution density and function of the following random variables: a) \( \tau_{1}=\sqrt[3]{\xi} \) b) \( \tau_{2}=-\xi^{2} \) c) \( \tau_{3}=0.5 \xi-1 \). 2. Calculate the expected values \( E\left[\tau_{3}\right], E\left[\tau_{2}\right] \).