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## Homework Statement

Let B

_{t}be a standard Brownian motion. Let s<t:

a) Compute [tex]P(\sigma B_{t}+\mu t|B_{s}=c)[/tex]

b) Compute [tex]E(B_{t}-t|B_{s}=c)[/tex]

## Homework Equations

Defition of brownian motion: B(t) is a (one-dim) brownian motion with variance [tex]\sigma^{2}[/tex]if it satisfies the following conditions:

(a) B(0)=0

(b) independent increments

(c) stationary increments

(d) B(t)~normal[tex](0,\sigma^{2}t)[/tex]

(e) [tex]t\rightarrow B_{t}[/tex] is continous

## The Attempt at a Solution

I know the policy is the attempt to do the problem, but I don't even know where to start. Maybe the definition of conditional probability?

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