QUESTION:

Compare and contrast the following distributions giving examples

1. Geometric and Negative Binomial distributions
2. Exponential and Gamma distributions

I don't understand how I would answer this had it come in an exam...

Do I derive one distribution from the other? Or simply state in the simplest of terms what makes each pair of distributions similar...?

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That must certaily be relative to what you have learnt in the course! For a starter, what is the distribution of an iid (independent and identically distributed) sum of exponencial variables? Which experiment you can do with flipping coins define a geometric distribution? Same with negative binomial? –  kjetil b halvorsen Nov 26 '12 at 19:33
Couple of points you use: a) Summation of the random variables (for example, what does summing of gemotric RV's produce versus summing of negative binmial rv's. b) if one is the special case of other? c) how do their MGF's relate to each other (related to (a)) d) you can gain extra credit (if possible) to show contrast between negative binomial and and gamma distribution (one can be considered as a discrete analog of the other) –  jay-sun Nov 26 '12 at 21:36
Why do you omit to answer ANY of the queries addressed at you in comments? –  Did Dec 2 '12 at 14:02