15.2.21 One dimensional random variables and their characteristics

Problem: When calculating the compound interests, the calculation of the real interest rate in terms of inflation is carried by the formula: \[ \tau=\frac{1+r}{1+\xi}-1 . \] The given (announced) gross rate is denoted by \( r \), and the rate of price growth for a year is denoted by \( \xi \). Assuming that \( \xi \) is a random variable, equally distributed on \( [10 \% ; 12 \%] \), find the distribution function of the real interest rate.