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From Probability to Statistics

  1. Suppose there is a process which produces identical computer chips and it is your job to determine the reliability of the process. You assume that the process produces a bad chip with probability $p$.
    1. Suppose you know that $p$ is $0.1$. What is the probability that in a selected 10 chips, no bad chips will be found?
    2. Suppose you test 10 chips and 5 are found to be bad. What is your estimate of $p$? How much would you expect the actual value of $p$ to vary from your estimate? What if you had tested 100 chips and found 50 to be bad?
    3. # Suppose you test 10 chips and none are found to be bad. What can you conclude about $p$? In particular, how big can $p$ so that this result is within a 95% interval?

Jon Shapiro