A variable x starts at zero and follows the generalized Wiener process dx = a dt + b dz
Where time is measured in years.During the first two years a=3 and b=4.During the following three years a=6 and b=3.What the standard deviation of the value of the variable at the end of 5 years
A) 6.2
B) 6.7
C) 7.2
D) 7.7

Question

Quizplus · Accepted Answer

The standard deviation of the variable at the end of 5 years can be calculated using the formula for the generalized Wiener process. The variance ($\sigma^2$) of the process after time $t$ is given by $b^2t$, and the standard deviation ($\sigma$) is the square root of the variance. For the first two years, $b=4$, so the variance contributed by these years is $4^2*2 = 32$. For the next three years, $b=3$, so the variance contributed by these years is $3^2*3 = 27$. The total variance over the 5 years is $32 + 27 = 59$. The standard deviation is the square root of 59, which is approximately 7.7.

A Variable X Starts at Zero and Follows the Generalized