Interview Question: A Tale of Two Related Distributions

Sample Question #158 (probability theory – distributions)

Explain the difference between the normal distribution and the student-t distribution. How’re the two distributions used empirically?

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One Response to Interview Question: A Tale of Two Related Distributions

  1. Brett says:

    ANSWER
     
    Well, first of all, they have different pdf’s! (It never hurts to mention the obvious when you answer such questions — if you didn’t, the interviewer might give you a really sarcastic or disdainful look.) What matters is the t distribution has fatter tails, i.e., higher densities in the extremes.  (Note, don’t say "higher probabilities," since these distributions are continuous.)
     
    Empirically, normal distribution is used as the underlying distribution of many different kinds of data populations, while t distribution is the one used for inferences on data samples.
     

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