# Stochastic Processes in Physics and Chemistry

Chapter03 - Home
Exercises: 1 - 2 - 3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12 - 13 - 14 - 15 - 16 - 17 - 18 - 19 - 20 - 21 - 22 - 23 - 24 - 25 - 26 - 27 - 28 - 29 - 30 - 31 - 32 - 33 - 34 - 35 - 36 - 37 - 38 - 39

Exercise. This is the solution to exercise 3.1.1 in the book.

Solution. The $n$-time average is:

The variance is:

${\sigma }^{2}\left(t\right)={\int }_{-\infty }^{\infty }Y{\left(t\right)}^{2}{P}_{X}\left(x\right)dx-{\left({\int }_{-\infty }^{\infty }Y\left(t\right){P}_{X}\left(x\right)dx\right)}^{2}$

The autocorrelation function is: