
15.2.29 One dimensional random variables and their characteristics
Problem:
A demand deposit account was opened in the amount of 20 thousand dollars at a simple annual interest rate of \( 1 \% \). While closing the account the depositor will get the sum: \( \tau=20000(1+0.01 \xi) \)
Experience shows that the time after which the depositor can close the account on such a deposit (random variable \( \xi \) ), can be approximated by an exponential distribution law with the parameter \( \lambda=2 \).
1. What is the average time spent on such a deposit?
2. What is the distribution density of the random variable \( \tau \) ?
3. What is the average variable of the obtained amount of money?