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Thread: Am in way over my head?

  1. #1
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    Am in way over my head?

    I started my MS Stats program at George Washington University this semester. The first course is Mathematical Statistics:

    This is the first part of a two semester course in Mathematical Statistics. Probability theory is presented as a mathematical foundation for statistical inference. Axiomatic probability is introduced then some standard discrete and continuous probability distributions are presented. Joint distributions and transformations are discussed. Probabilistic convergence concepts are introduced.
    The only requirements for the course are Multivariable Calculus and Linear Algebra, both of which I recently completed (that is as far as my mathematical education goes). I am finding the course to be impossibly difficult, to the point where I am only able to answer certain problems because their solution is either available online or because I am spending hours upon hours on them. This is giving me serious concern because I am not sure I'd be able to answer most of the questions on a midterm or the final. I'm not talking about not getting an A- in the course, but really just not being able to answer more than 25% of a test.

    For example, attached is the HW we got for the second week, after we did combinatronics. I feel like I can follow what the professor is lecturing and what is being explained in the book, but am at a loss when it comes to applying it. It seems like most if not all of the students in the class had Math majors or minors in college, but if that is required to be successful in the program then I am not sure why I was admitted into it.

    I was wondering if people have completed similar degrees or courses and could share their experience. This course is also required for the PhD students, though there are none in the class. Do most of the students just muddle along like I am, or is this something that they are not struggling with given they know so much more maths?


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  2. #2
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    Re: Am in way over my head?

    Hey vashts85.

    I double majored in mathematics and statistics and the questions you posted were quite common in the serious introductory courses in probability (i.e. 2nd year undergraduate).

    If you haven't done a lot of mathematics before then I'm not surprised this is happening to you. Basically you need to get some intuition so that you can step back and see the forest from the trees.

    I can give you some pointers that might help you do this (i.e. see the forest from the trees).

    In probability we have the actual theory (which is the Kolmogorov axioms, the major theorems and results), the models (i.e. that are used to describe an actual process), and the connection to the real world. All have connections to each other and one must have all perspectives when looking at a problem.

    In mathematics we have representation (structure), transformation (changing something), and constraints (choosing the possibilities being considered). You also have in addition to this language (since a lot involves manipulation of symbols in a mathematically consistent manner) and the ideas that help form and explain what is said in the language. Looking at mathematics without the ideas is like trying to learn Russian by just reading Russian books - the ideas are what bridge your understanding of the mathematical symbols and phrases to something that makes sense.

    Understanding probability means understanding what it really is. Probability can relate to the real world through stochastic processes (i.e. processes in the real world that exhibit random properties) and it could be part of a theoretical model used for understanding probability or even doing statistics (these are known as sampling distributions). What you need to understand is how to look at a probability space and know how to get the events in that space.

    Getting the events in the space will also help you with conditional probability and once you connect the events to probability models and ideas things will get a lot easier. A conditional probability is basically a probability where you look at a subset or "slice" of the data. Once you understand this using conditional probabilities will be a lot easier.

    I would advise you to understand when to focus on the mathematical aspects and when to focus on the real world aspects. Mathematics for the most part in these courses is playing with symbols and ideas so you can get from one point (the start of the question) to the other (the answer).

    In going from start to finish you have to take all the information you are given or assumed and use the representation, transformation, and constraints (as talked about above) to get closer and closer to the final answer. Every piece of information you have will impact the choice of these three things at each step. Once you do this enough it will get a lot more intuitive.

    I would also advise you not to use your mental intuition for probability - this will make things a lot more difficult for you. Understand the intuition of the axioms and get used to them instead of using your mental intuition - because it can often get you into a mess.

    With the axioms the best thing I can recommend is to understand how to break a probability space down into its simplest events. Once you can do this then you can use the axioms to get probabilities of events of any complexity and slowly you can look at complicated models and understand how they derived and possibly even derive ones that aren't in the textbook.

    If you have any more questions I can do my best to answer them.
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