15.2.15 One dimensional random variables and their characteristics

Problem: It's known that the continuous random variable \( \xi \) is distributed according to the exponential distribution law with the parameter \( \lambda=0,2 \). Find the laws of distribution in the form of a density and distribution function of the following random variables: \[ \begin{array}{l} \text { 1. } \tau_{1}=\sqrt{\xi} \\ \text { 2. } \tau_{2}=\xi^{2} ; \\ \text { 3. } \tau_{3}=0,5 \ln (\xi) . \end{array} \] Calculate their numerical characteristics.