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Thread: A conditional Pobability Problem

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    A conditional Pobability Problem



    Please see the attached plot to understand clearly the problem

    I am struggling with a conditional probability problem, i would appreciate if someone can give me an answer, idea, insight...whatever guide me to solve it.
    Here the description of this problem:
    i have the output voltage of a sensor plotted versus time t, and i have 7 levels of voltages. I would like to plot the probability of each level of being activated (voltage > the level).what i did as a first solution is to sum up the time for each level (only times when the level is activated) so i got seven different values(t1,t2,t3, t4,t5,t6,t7).Then i sum up those 7 values to got a total time t=t1+t2+t3+t4+t5+t6+t7, then i defined the probability as p(level i)= ti/t ;i=1,2,3,4,5,6,7.
    my problem is that i am not sure if this is right, since there are conditional probabilities to be counted (for example p(k+1/k)), k=1,2,3,4,5,6).
    how to define the right probability?
    p(k+1/k): probability that level K+1 is activated knowing that level k is activated.
    Attached Images  

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    The first model that you use is a multinomial model, which assume that the voltage level
    in each time unit is independent from other.

    The second model that you are concern of is like some time series data that each data
    in the series are actually correlated with one or more data in that series.

    So you better check the physical properties that the assumption of independence is
    valid or not. If thats not proper to make such assumption, then we have to investigate
    a more complicated "time series" model.

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    Thank you BGM, here are more explanations:
    We implement a sensor into a structure to measure the strain each time the structure is subjected to a loading (loads vary). Depending on the amount of the loading, a certain number of gates will start recording the strains. Here each gate correspond to a level (7 levels--->7 gates). For example, a load P can open one or more gates. If more than one gate are recording, the first gate is automatically recording since its has the minimum level. Let`s say 3 gates are recording---> 3 first levels are reached, than when i count the time, there is a common period of time for the three gates recording together (as you can see on the voltage plot). and when counting the times for each gate, i feel that this time is repeated, and i guess here comes the dependency...
    don`t you think so?
    should i look for more complicated time series?
    thank you again for the help

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