- #1

fluidistic

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**1. Homework Statement +Relevant equations+Attempt at a solution**

Hi, I'm stuck on a problem.

I have that [/itex]P(x,t|y,0)[/itex] represents the probability density that a function has the value x at time t knowing it had the value y at time [/itex]t_0=0[/itex] .

Where [itex]P(x,t|y,0)=\frac{1}{\sqrt{2\pi t}\sigma} \left[ \exp \{ - \frac{(x-y)^2}{2\sigma ^2 t} \} -\exp \{ - \frac{(x+y-2B)^2}{2\sigma ^2 t} \} \right][/itex]

Given [itex]B\geq x[/itex], [itex]B>y[/itex] and both x and y are not worth negative infinite, I'm interested in calculating the probability that the event will happen (i.e. that x=B) at some time.

Worded differently and adding some extra information, the mean time for the event to happen is infinite, nonetheless the probability for it to happen at some time is 1. I don't know how to prove the latter.

If I'm not wrong and I evaluated well the units, the units of [itex]P(x,t|y,0)[/itex] are [itex]1/\sqrt V[/itex]. While x and y have units of voltage (V).