- #1

tom.stoer

Science Advisor

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## Main Question or Discussion Point

I have a problem calculating the following probability.

There are two signals A and B each consisting of a series of "pulses" at times

{t

{t

The signal A is "on" in the time intervals [t

There is a given probability for the signal A to be "on" depending on the (random) times between the pulses; the same applies for the signal B.

How can one calculate the probability that for a certain time T

There are two signals A and B each consisting of a series of "pulses" at times

{t

^{A}_{0}, t^{A}_{0}+Δt, t^{A}_{1}, t^{A}_{1}+Δt, t^{A}_{2},t^{A}_{2}+Δt, ...} and{t

^{B}_{0}, t^{B}_{0}+Δt, t^{B}_{1}, t^{B}_{1}+Δt, t^{B}_{2}, t^{B}_{2}+Δt,...}The signal A is "on" in the time intervals [t

^{A}_{n}, t^{A}_{n}+Δt], and it's off in the time intervals [t^{B}_{n}+Δt, t^{B}_{n+1}].There is a given probability for the signal A to be "on" depending on the (random) times between the pulses; the same applies for the signal B.

How can one calculate the probability that for a certain time T

*both*signals are "on"