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Markov Decision Processes

First let’s have a framework for what we would call randomness throughout time. Stochastic Procesess A Stochastic Process is defined as a collection of random variables $ \{\ X(t)\}_{t \in T}\ = \{\ x_1 , x_2 , \dots , x_T \}\ $ indexed by time (the subscript). When for all elements of this collection assume a value, we call each value in thi...

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Matrix Multiplication

Remember the good ol days when 6 x 5 easily made sense as adding 6 together with itself 5 times and whala you ended up with 30. Now you’re in college and things are hard :( Hopefully running through an example can give you a bit of a glimpse as to how and why we do matrix multiplication. How to Compute Matrix Multiplication Consider two Matric...

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Bayes Theorem and ROC

Conditional Probability Is the idea of understanding the probability an event A occurs given an event B. We formally say the Conditional Probability of A given B is defined as: \[P(A | B ) = \frac{P(A \cap B)}{P(B)}\] Photo Courtesy of [“Conditional Probability and Independent Events”] Pictorially we consider the 3 ...

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Combinations

Since the concept of “n choose k” seems to appear a lot in my life I decided I would make a quick post explaining the intuition behind it. Let’s start with a simple example. Say we had a set of three greek characters representing the names of three friends, $ F = { \alpha, \beta, \gamma }$ and we are interested in knowing how many uniquely pair...

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The Convolution Integral

Since signals are sets of data or information and systems process said data, we are interested in the analysis of systems. When we deal with a special type of system that contains the properties of linearity and time-invariance, we are able to construct methods of analysis that are extremely useful for Linear Time-invariant (LTI) systems. Fourie...

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Random Variables and Distributions

I hope this article serves as a basic introduction to the terminology of probability theory! Random Variables Considering that an experiment is a procedure that produces well defined outcomes, like taking a course and finishing with a certain grade letter, we see that a random variable is a function which maps random outcomes from experiments ...

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Connecting to UC Davis Library VPN on Ubuntu

You might be wondering why all this is necessary to do. Lots of services and features such as the New York Times and Textbooks are available to UC Davis students only if they have physical access to the Campus wifi. UC Davis Virtual private network service or VPN, serviced by the Information and Educational Technology department, mitigate this p...

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Compiling C code and submitting to CSIF

If you were anything like me, you were struggling a lot to submit your homework. Mainly since you had no idea what CSIF is and you have not coded anything in C before. Just follow along and you will be able to complete the homework assignment. In this tutorial I am using Ubuntu 18.04.4 LTS release and adding onto what Professor Wu has told us. ...

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