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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…
<em>z</em> 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
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
Biological radiation dose can be estimated from dicentric chromosome frequencies in metaphase cells. Performing these cytogenetic dicentric…

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