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Assume a bernoulli random variable with success probability p. In 12 independent trials of the bernoulli I only look at the third, sixth, nineth and twelfth experiment. What is the expected value of the number of successes that I observe at these four occasions?

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Since the trials are independent, the expected value is still $p$.

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  • $\begingroup$ you mean $4p$ I assume? $\endgroup$
    – user83346
    Commented Mar 6, 2016 at 9:50
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    $\begingroup$ You wrote "What is the expected value of the number of successes that I observe at these four occasions?", then at each occasion the expected value is $p$. Of course, if you want to know the expected number of success in these four occasion, it is $4p$. $\endgroup$ Commented Mar 6, 2016 at 9:55
  • $\begingroup$ OK I see your point. +1 $\endgroup$
    – user83346
    Commented Mar 6, 2016 at 9:58

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