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I'm not sure a probablist is a correct term. I would like to consider the difference between a statistician and a specialist in probability theory.

The short answer is the statistician works with data while the specialist in probability theory works more with individual assumed or known probabilities.

Here's the longer answer:

The statistician typically is seeking to draw conclusions from collected data. The discipline of statistics includes all phases of a study, from design, collection, analysis, and presentation. A statisician however, may also try to improve the methods of analysis, so he will be involved in probability theory.

The statistician may work in many fields, including medicine, epidemiology, pharmacy (tests of new drugs), engineering, insurance, sociology, marketing.

The specialist in probability theory (or probability theorist) may draw conclusions from an understanding or reasonable assumptions of the outcome of a system or probability of events from an understanding of the probability of underlying components.

This might sound a bit complicated, but the specialist can tell you how much you can expect to lose if you play the lottery, or any other game of chance. He does this by knowing the probabilities of the underlying event of chosing a winning number.

The related link mentions two area of applications: risk analysis and commodities trading. More broadly, the areas of probability analysis using both Monte-Carlo simulation and analytical means, have applications in many areas environmental systems, operations research applications, valuation of financial derivatives involving risk, and more recently, stochastic simulation of chemical reactions and bioinformatics (computer related work with DNA).

Please check the related links. You can find much more from links on the internet.

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Q: What is the difference between statistician and a probabilist?
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