The probability density function of a biased random walk in 0 x 1/2 is: P(x, t)...

Transcribed Image Text:

The probability density function of a biased random walk in 0 x 1/2 is: P(x, t) = Ne-(vt-2x) e cos(x), where v is a constant drift and N is a constant. (a) By imposing an appropriate condition at t = 0, find the constant N. Hint: You may find the following integral useful: [ ex cos bar da = (a cosbx + b sin bx). eax a +6 (b) Find the first-passage probability density function F(t) of this random walk, the mean exit time 7, and show that when |v| < < 1: T -= TO (1-1=1). where To is the mean exit time when v = 0. The probability density function of a biased random walk in 0 x 1/2 is: P(x, t) = Ne-(vt-2x) e cos(x), where v is a constant drift and N is a constant. (a) By imposing an appropriate condition at t = 0, find the constant N. Hint: You may find the following integral useful: [ ex cos bar da = (a cosbx + b sin bx). eax a +6 (b) Find the first-passage probability density function F(t) of this random walk, the mean exit time 7, and show that when |v| < < 1: T -= TO (1-1=1). where To is the mean exit time when v = 0.