The And Of A Bernoulli Random

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Abstract
Abstract here
Humans, and animals, often perceive events as being random. Many lab oratory and controlled studies have been conducted over the last half-century to determine human ability to detect whether a particular string of events is random. Often, these studies consist of detecting whether some binary sequence has the properties of a bernoulli random variable. From the re sults of these studies, we can conclude experimental subjects hold the Law of
Small Numbers (Tversky & Kahneman, 1971) to be true. Particularly, many studies have found humans have a skewed perception of and researchers do not understand randomness. In this paper, we seek to answer three focused questions: 1. Can randomness be defined, and if so, how can humans determine whether a sequence is random?
2. What have previous studies concluded with regard to decision makers skill in determining whether a sequence is random?
3. Are we able to develop a rigorous, mathematical argument regarding randomness? Before we begin to answer these questions, we will present definitions from the literature to facilitate the discussion.
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1 Definitions
Two ubiquitous concept used in studies of randomness are ”the gambler’s fal lacy” and ”the hot hand.” Using the definitions from Oskarsson, van Boven,
McClelland, and Hastie (2009), we will define the gambler’s fallacy as the judgement ”the streak will end.” The gambler’s fallacy is also known as neg ative recency. The hot hand is the judgement that ”a streak will
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