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Probability and Statistics
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The learner will be able to use chance devices such as spinners and dice to generate and analyze the probability of an event. LEARNER OBJECTIVES: 1) organize and interpret data in various forms; 2) use tally marks to organize a group of data; 3) interpret object and pictorial graphs to display objects and information; 4) determine, interpret, and predict probability; 5) interpret concepts of chance; 6) calculate the odds governing the occurrence (positive or negative) of a given event.
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Fundamentals of Probability, Statistics, Experiments and Data This discusses the history and nature of "What are Probability and Statistics?" The nature of data (types of data—discrete versus continuous, categorical, etc.) is discussed, as well as topics of problems in data gathering, unintended outside forces getting confounded with the data, etc.
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While the biometricians and statisticians were using the normal distribution, the probability theorists were developing ever more refined versions of the central limit theorem. (Although the term central limit theorem (q.v.) dates from the early 20th century, the subject begins with Laplace.) Where modern statistical notation for the normal differs from Fisher's, the changes mainly reflect the influence and prestige of modern probability theory.
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In every case, the peak probability is at half the number of flips and declines on both sides, more steeply as the number of flips increases. This is the simple consequence of there being many more possible ways for results close to half heads and tails to occur than ways that result in a substantial majority of heads or tails. The RPKP experiments involve a sequence of 1024 random bits, in which the most probable results form a narrow curve centred at 512. A document giving probabilities for results of 1024 bit experiments with chance expectations greater than one in 100 thousand million runs is available, as is a much larger table listing probabilities for all possible results.
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Introduction to Statistical Analysis Statistical Analysis reviews some fundamental summary statistics and then begins to relate sample statistics with their parallel components in probability. (Sample mean to probability mean, sample variance to variance, etc.) Concepts of confidence intervals and hypothesis testing are introduced with simple examples of each.
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This is a standard introduction to probability and statistics. If you are new to probability or you can't remember what a probability density function is, this is the perfect book for self study.
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