The Angry Statistician

The Higgs boson is the smallest detectable wave in the Higgs field . Interacting with the Higgs field causes  articles to acquire inertial mass; without the Higgs field, no particle would have inertial mass. Some particles don't feel the Higgs field at all ( photons ) and so are massless; some feel it very lightly ( neutrinos ) and have little mass; ordinary particles feel it strongly. In physics the current best understanding of the forces (excluding gravity) is called the Standard Model . The one remaining elementary particle in the Standard Model that hasn't been experimentally detected is - the Higgs boson. The Standard Model describes these forces: Electromagnetism (attraction/repulsion due to electric charge) Weak force (causes radioactive decay) Strong force (holds quarks together to form protons,neutrons) Electromagnetism is the unification of electricity and magnetism, which were originally thought to be two different forces. The next steps in phys...

Quantum Mechanics and Quantum Computation About the Course Quantum computation is a remarkable subject, and is based on one of the great computational discoveries that computers based on quantum mechanics are exponentially powerful. This course aims to make this cutting-edge material broadly accessible to undergraduate students, including computer science majors who do not have any prior exposure to quantum mechanics. The course will introduce qubits (or quantum bits) and quantum gates, the basic building blocks of quantum computers. It will cover the fundamentals of quantum algorithms, including the quantum fourier transform, period finding, and Shor's iconic quantum algorithm for factoring integers efficiently. The course will also explore the prospects for quantum algorithms for NP-complete problems and basic quantum cryptography. The course will not assume any prior background in quantum mechanics. Instead, it will use the language of qubits and quantum gates ...

Dive Into Python Google's Python Class Learn Python The Hard Way

I've created a GitHub repository for some fun simulations and other code to illustrate ideas and applications. I  believe it's helpful for many people to use simulations to better understand what's going on when learning statistics. Why are things done the way they are? Well, let's simulate the random process and find out! These are currently in Python but I'll be adding R versions. I'll be adding simulations that illustrate particular ideas in probability and statistics, or that are just fun. Some of the most interesting and useful, I believe, will be related to hypothesis testing. The initial repository has a basic Monty Hall simulation and two roulette simulations that sample from either a uniform or exponential distribution. I tend to use NumPy quite a bit. sim-udacity on GitHub

For any problem involving conditional probabilities one of your greatest allies is Bayes' Theorem . Bayes' Theorem says that for two events A and B, the probability of A given B is related to the probability of B given A in a specific way. Standard notation: probability of A given B is written \( \Pr(A \mid B) \) probability of B is written \( \Pr(B) \) Bayes' Theorem: Using the notation above, Bayes' Theorem can be written:  \[ \Pr(A \mid B) = \frac{\Pr(B \mid A)\times \Pr(A)}{\Pr(B)} \] Let's apply Bayes' Theorem to the Monty Hall problem . If you recall, we're told that behind three doors there are two goats and one car, all randomly placed. We initially choose a door, and then Monty, who knows what's behind the doors, always shows us a goat behind one of the remaining doors. He can always do this as there are two goats; if we chose the car initially, Monty picks one of the two doors with a goat behind it at random. Assume we pick Door 1 an...

A (Brief) History: The Monty Hall problem is arguably the most infamous probability puzzle in recent history. It was originally proposed in its current form in 1975, but only really surged into the public spotlight in 1990 when in appeared in a Parade column written by Marilyn vos Savant . For more details on the history of this problem see Wikipedia: Monty Hall problem . The Original: As given in Marilyn's column the problem read: Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1 [but the door is not opened], and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice? The phrasing here is ambiguous. Does Monty always  show you a goat? Does he only show you a goat when switching would lead to a win? Does he only...

Here's a nice problem I encountered in a course on applied stochastic processes. Problem: Show that the set of all pairs of positive integers can be placed into one-one  correspondence with the positive integers by giving an explicit one-one mapping  between the two sets. Solution: This can be done expediently using the theory of partial difference equations.  A standard diagonalization can be characterized by the following  relations: \( f(1,1)=1 \) \( f(x,y) = f(x-1,y)+x+y \) \( f(x,y) = f(x,y-1)+x+y-1 \) These can be written in difference notation as: \( f(1,1)=1 \) \( \frac{\Delta f}{\Delta x} = x+y \) \( \frac{\Delta f}{\Delta y} = x+y-1 \) Equation 2 gives \( \frac{{\Delta}^2 f}{{\Delta x}{\Delta y}} = 1 \) and equation 3 gives \( \frac{{\Delta}^2 f}{{\Delta y}{\Delta x}} = 1, \) so this is an exact partial difference equation. Summing using equation 2, \[ f(x,y) = x(x+1)/2 + xy + g(y). \] Differencing and setting this equal to equation...