Time: 20 minutes. This quiz is open book, open notes. You must provide reasons for your answers. Estimated problem-solution times are provided as a hint.
1. Estimate the probability that a Binomial(400, 0.05) variable will not exceed 30. Justify your approximation method. (Three minutes.)
The figure shows PDFs for four distributions. Number 1
is symmetric, number 2 has the lowest peak, number 3 is discontinuous, and
number 4 has many modes. Distributions #1 and #2 have infinite support,
but almost all their probability is concentrated within the region shown here
and their tails continue to decrease rapidly outside the region shown. #3
and #4 have finite support contained within the region shown here.
2. Which distribution has the smallest third central moment? Which one the largest? (One minute.)
3. Of these four distributions, which one(s) will have the largest 12th central moment? (15 seconds.)
4. (Extra credit) Estimate the probability that a Binomial(400, 0.05) variable will equal 0. Justify your estimate. (Three minutes.)
Scoring: The passing score is 90.
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