Recent content by theCoker

Solution a) P(\sigma B_{t}+\mu t=a|B_{s}=c)=P(B_{t}=\frac{a-\mu t}{\sigma}|B_{s}=c)=\frac{P(B_{t}=\frac{a-\mu t}{\sigma},B_{s}=c)}{P(B_{s}=c)}=P(B_{t}-B_{s}=\frac{a-\mu t}{\sigma}-c=f_{t-s}(\frac{a-\mu t}{\sigma}-c) b)...

From what the Prof. said today (last day of class)... X_{t}=\sigma B_{t}+\mu t where X_{t} is "Brownian motion with drift" and \mu t is the "drift term". It was also said that X_{t}~Normal(\mu t, \sigma^{2}t).

a) is stated exactly as my professor posed the question.

assuming you are referring to (a) and not a): (a) B(0)=0, *a convenient normalization. sorry about that. thanks for the thoughts. assignment is due now =[ however, i am puzzled by this problem and would appreciate more thoughts.

Homework Statement Let Bt be a standard Brownian motion. Let s<t: a) Compute P(\sigma B_{t}+\mu t|B_{s}=c) b) Compute E(B_{t}-t|B_{s}=c) Homework Equations Defition of brownian motion: B(t) is a (one-dim) brownian motion with variance \sigma^{2}if it satisfies the following conditions: (a)...

You seem to have made an error in applying the quotient rule. You should have f'(x)=[g'(x)h(x)-h'(x)g(x)]/[h(x)]^2 where g(x)=x^2 and h(x)=1-x^2. After you differentiate h(x) where I suggested, multiply the resulting numerator all out and combine like terms. I confirmed the answer to a) but...

Well, I got some help from elsewhere, but thought I might post the solutions anyway. part a. solution Expected number of trains from 1 to 3 =(2hrs) x (4 per hour) = 8 trains. part b. solution E[T]=1/(lambdatrains + lambdabuses)=1/12=5minutes. part c. solution (24 passengers/bus) x...

I had this problem on my last midterm and received no credit for these parts. 1. Express trains arrive at Hiawatha station according to a Poisson process at rate 4 per hour, and independent of this, Downtown local buses arrive according to a Poisson process at rate 8 per hour. a. Given that 10...