An Introduction to Probability Theory and its Applications, Volume I

TL;DR: This chapter discusses quantum information theory, public-key cryptography and the RSA cryptosystem, and the proof of Lieb's theorem.

TL;DR: RTP provides end-to-end network transport functions suitable for applications transmitting real-time data over multicast or unicast network services and is augmented by a control protocol (RTCP) to allow monitoring of the data delivery in a manner scalable to large multicast networks.

TL;DR: In this article, a survey of elementary applications of probability theory can be found, including the following: 1. Plausible reasoning 2. The quantitative rules 3. Elementary sampling theory 4. Elementary hypothesis testing 5. Queer uses for probability theory 6. Elementary parameter estimation 7. The central, Gaussian or normal distribution 8. Sufficiency, ancillarity, and all that 9. Repetitive experiments, probability and frequency 10. Advanced applications: 11. Discrete prior probabilities, the entropy principle 12. Simple applications of decision theory 15.

TL;DR: This work addresses the problem of predicting a word from previous words in a sample of text and discusses n-gram models based on classes of words, finding that these models are able to extract classes that have the flavor of either syntactically based groupings or semanticallybased groupings, depending on the nature of the underlying statistics.

TL;DR: In this article, a Monte Carlo simulation is performed to calculate a probability of the difference between the average value in some random sample and the average over the total set, which is used to compare the available information with the official results.

TL;DR: In this article, the authors studied the distribution of the color of a matching pair by looking at two methods for selecting socks: one method is memoryless and effectively samples socks with replacement, while the other samples socks sequentially, with memory, until the same color has been seen twice.

TL;DR: Three different problems in order statistics are considered in this dissertation and it is shown that recurrence relations valid for independent and identically distributed random variables continue to hold for exchangeable variables.