MathProblemsBank

15.2.22 One dimensional random variables and their characteristics

Problem: The amount of money that a bank depositor, who has put 1000 dollars into his account, will get in three years, is calculated by the formula: \[ \tau=1000(1+\xi)^{3} . \] The annual interest rate, which, according to the conditions of the agreement, can be changed by the bank unilaterally, is denoted by \( \xi \). Assuming that the random variable \( \xi \) is equally distributed on the segment \( [0.5 \% ; 2 \%] \), Find the distribution law in the form of density and the distribution function of the random variable \( \tau \). Calculate the expected value and the dispersion \( E[\tau], V[\tau] \).