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# Chapter 6 Probability Distributions

## Probability in Statistics

Probability is the likelihood of an event occurring. The term event is defined as a collection of results of a procedure. An event is a simple event…

## Random Variables

A random variable is a single numerical value that indicates the outcome of a procedure. The concept of random variables is fundamental to the…

## Probability Distributions

The probability of a random variable x  is the likelihood of its occurrence. A probability distribution represents the probabilities of a…

## Probability Histograms

A probability histogram is a visual representation of a probability distribution. Similar a typical histogram, the probability histogram consists of…

## Unusual Results

Unusual results are those that have a very low chance of occurring. Unusual results can be identified using probabilities and the range rule of…

## Expected Value

The expected value is known as the "long-term" average or mean. This means that over the long term of experimenting over and over, you would…

## Binomial Probability Distribution

A binomial distribution is a probability distribution for a procedure with a fixed number of trials, where each trial can have only two outcomes. The…

## Poisson Probability Distribution

A Poisson probability distribution is a discrete probability distribution. It gives the probability of a number of events occurring in a fixed…

## Uniform Distribution

The uniform distribution is a continuous probability distribution of events with an equal probability of occurrence. This distribution is…

## Normal Distribution

The normal, a continuous distribution, is the most important of all the distributions. Its graph is a bell-shaped symmetrical curve, which is…

## z Scores and Area Under the Curve

z scores are the standardized values obtained after converting a normal distribution into a standard normal distribution. A z score is measured in…

## Applications of Normal Distribution

The normal distribution is a useful statistical tool. One of its practical applications is determining the door height after considering the normal…

## Sampling Distribution

Given simple random samples of size n from a given population with a measured characteristic such as mean, proportion, or standard deviation for each…

## Central Limit Theorem

The central limit theorem, abbreviated as clt, is one of the most powerful and useful ideas in all of statistics. The central limit theorem for…

## Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level

We demonstrate a method for the synthesis of cyclic polymers and a protocol for characterizing their diffusive motion in a melt state at the single…

## Rare Event Detection Using Error-corrected DNA and RNA Sequencing

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Conventional next-generation sequencing techniques (NGS) have allowed for immense genomic characterization for over a decade. Specifically, NGS has…

## Expedited Radiation Biodosimetry by Automated Dicentric Chromosome Identification (ADCI) and Dose Estimation

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Biological radiation dose can be estimated from dicentric chromosome frequencies in metaphase cells. Performing these cytogenetic dicentric…

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