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Math Help - confidence interval for bernoulli(?)-like trials

  1. #1
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    confidence interval for bernoulli(?)-like trials

    Hi!

    Let's say we have a counter, set to 0 initially.

    Let's say we conduct experiment where in each trial a counter may be increased by 1 with known probability p.

    E.g. if p = 0.8 then after the 1st trial the counter will be 1 with probability 0.8 and 0 with probability 0.2. After the 2nd trial, the counter will contain 0 with probability 0.04 (0.2 * 0.2), 1 with probability 0.32 (2 * 0.2 * 0.8) and 2 with probability 0.64 (0.8 * 0.8).

    Now, with given probability of success (== counter increment) p and number of trials n, does it make sense to construct a confidence interval around the expected final counter value? If yes, then how? If no, what would be another way to communicate confidence in this case?

    This is actually a simplified description of a research experiment I'm involved in. I need to give prediction on the counter value after a large number of trials. Intuitively I think that the expected value of the counter would be p^n, but how do I state my level of confidence in it?

    Suggestions and links are appreciated. Thanks!
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by wadcom View Post
    Hi!

    Let's say we have a counter, set to 0 initially.

    Let's say we conduct experiment where in each trial a counter may be increased by 1 with known probability p.

    E.g. if p = 0.8 then after the 1st trial the counter will be 1 with probability 0.8 and 0 with probability 0.2. After the 2nd trial, the counter will contain 0 with probability 0.04 (0.2 * 0.2), 1 with probability 0.32 (2 * 0.2 * 0.8) and 2 with probability 0.64 (0.8 * 0.8).

    Now, with given probability of success (== counter increment) p and number of trials n, does it make sense to construct a confidence interval around the expected final counter value? If yes, then how? If no, what would be another way to communicate confidence in this case?

    This is actually a simplified description of a research experiment I'm involved in. I need to give prediction on the counter value after a large number of trials. Intuitively I think that the expected value of the counter would be p^n, but how do I state my level of confidence in it?

    Suggestions and links are appreciated. Thanks!
    After 100 trials with a probability 0.8 of increment per trial the expected count is 80. In general it is np, and its SD is \sqrt{np(1-p)}.

    RonL
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