In probability theory, the birthday paradox is an interesting problem in that it is an easy vehicle to grasp several important statistical concepts like likelihood and combinatorics and the surprising conclusion it arrives.
The problem of the birthday is simple, in a room with n people, how many of them will have to same birthday? It turns out, using the following equation, it only takes 23 people to reach a 50% probability of having two people with the same birthday.
In the study of quality control, sampling is an important technique to assess the overall quality level of a lot of production run. Operating characteristic curve is a great tool to understand the quality profile of acceptance sampling.
In TI Nspire, the OC curve can be defined as following using binomial distribution as an alternative to hypergeometric distribution.
With the function defined, visualizing of 10% failure rate and sampling size of 20 can be done by graphing this function.
Interesting results from a recent paper presented at the 25th ACM conference on Computer and Communications Security shown advances in Generative Adversarial Network (GAN). In particular the paper focused on tackling Captcha with GAN. GANs take a game theory approach in the training of network and during the deep learning process two entities compete in a game that one trying to fool the other while the other strives not to be fooled.
Comparison of performance of machine learning the probability distributions are usually considered as metrics for benchmark. One such commonly used is the Jensen–Shannon Divergence and a generalization can be given as
The TI Nspire calculator is a great platform for visualizing data via interactive graphs. The built-in facility like input slider for variable value adjustment allowed dynamic visualization to complex equations, like the volatility sensitivity in delta-hedged gains used financial investment. Since this strategy involved a single call option, the volatility exposure equals the vega value of the option.
The following setup on the Nspire provided the functions to calculate the vega values.
This spreadsheet input screen stores the spot prices and the calculated Black Scholes vega values.
Finally, with the data plotting screen the graph of Delta hedged gains of volatility sensitivity is completed. An additional slider control can easily be added on it to adjust an offset variable so as to visualize scenarios under different spot price.
The Variance Inflation Factors function is available in R for determining existence of multicollinearity. The VIF function is given by:
And to use this built-in function is R:
The Movidius compute stick is supported on the Raspberry Pi 3 Model B platform. This is almost like a dream deployment for low power consumption applications. The overall dimension of Movidius with Raspi in their original configuration might not fit into some commonly available IP56 waterproof enclosures but with some ultra short extension cables and converters, packing them insides and even with a lithium battery pack should be easy.
The Supply Chain optimization is a classic sample in linear programming. The Microsoft Solver Foundation comes with an example on solving this problem in Excel.
The data are categorized and neatly listed out in one worksheet, while the Model pane provided interface for constraints settings. Unlike in the standard Excel Solver, the modelling is a bit more complex, but the interface helped by providing an organized and consistent user interface in Excel.