Regarding Research in Artificial Intelligence Which mathematical areas are important for research purposes in artificial intelligence? Specifically, If I have Masters in Statistics how much it will be beneficial for research in artificial intelligence? 
 A: @TonySF is correct that AI is a very diverse field. At this point it does not seem possible to predict what directions AI may take. So specific answers to your question must be speculative.
Almost certainly, an MS in statistics will be helpful. I think there are two aspects to the usefulness of statistics.
First, your MS should have given you practice in the appropriate use of mathematical ideas to solve real-world problems. Second, in my view, AI has
not paid enough attention to methods of validating what seems to be 'progress'.
Statisticians are accustomed to looking for methods of valid inference from
data. Obviously, not all methods of statistical analysis will transfer directly to AI, but the experience of seeking objective standards for success should be useful. (Also, particularly if your background in statistics has been exclusively frequentist and based on probability models, you should be open to Bayesian and algorithmic approaches.)
A strong background in computer science is essential in most AI activities,
both the theoretical CS background and skill in writing programs for specific
purposes. 
Some recent successes in AI seem to have come from a deeper understanding of
neurology and some aspects of psychology. My personal guess is that this trend
will continue, so you should be alert to the specific concepts in these areas
that you may need to study in depth.
Finally, it seems that quantum computation may soon be in widespread use. My
guess is that quantum computation will become increasingly important in some parts of AI. If you have any background in physics, it might be worthwhile to
learn more about quantum mechanics as applied to CS and, based on that, to try to understand
how new developments in quantum computation may be especially important in AI.
A: The only branch of Artificial Intelligence I can speak confidently about is Machine Learning. If you have a Masters in Statistics I am sure you have covered Linear Regression. This is perhaps the simplest example of Machine Learning. If you have covered Logistic Regression, then you also know something about classification problems, perhaps the most common type of problem in Machine Learning. If you do not have a thorough understanding of Linear and Logistic Regression, I suggest that you gain one now. Modern regression and classification methods can be much more sophisticated.
You will need a deep understanding of Linear Algebra and Multivariate Calculus. These will form the foundation. If your Masters program did not cover these topics in depth, you will need to make up for this. If your goal is to develop and implement new methods, you will need a good understanding of Algorithms and Data Structures from Computer Science, and Optimization techniques. Most of the optimization methods you'll need are based on Linear Algebra and Multivariate Calculus.
Edit: The rest of this answer has been removed because it was too uncharitable to the other answer.
