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The standard normal distribution, also called the Z-distribution, is a normal distribution with a mean of 0 and standard deviation of 1. To convert a random variable X with mean μ and standard deviation σ to the standard normal form Z, we calculate (X - μ)/σ. The normal distribution is widely used in statistics because many sampling distributions and transformations of variables tend toward normality for large samples. It also finds applications in approximating other distributions and in statistical quality control.

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Normal distribution

Normal distribution

Discrete distributions: Binomial, Poisson & Hypergeometric distributions

Discrete distributions: Binomial, Poisson & Hypergeometric distributions

The Normal Distribution

The Normal Distribution

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Normal distribution

The document discusses the normal distribution, which produces a symmetrical bell-shaped curve. It has two key parameters - the mean and standard deviation. According to the empirical rule, about 68% of values in a normal distribution fall within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. The normal distribution is commonly used to model naturally occurring phenomena that tend to cluster around an average value, such as heights or test scores.

Discrete distributions: Binomial, Poisson & Hypergeometric distributions

The PPT covered the distinguish between discrete and continuous distribution. Detailed explanation of the types of discrete distributions such as binomial distribution, Poisson distribution & Hyper-geometric distribution.

The Normal Distribution

The document discusses the normal distribution and some of its key properties. It also discusses the central limit theorem and how the distribution of sample means approaches a normal distribution as the sample size increases. Additionally, it covers how to transform a normally distributed variable into a standard normal variable using z-scores and how the normal distribution can be used to approximate the binomial distribution through a correction for continuity.

Review on probability distributions, estimation and hypothesis testing

This document provides an overview of probability distributions, estimation, and hypothesis testing. It discusses key concepts such as:
- Common discrete and continuous probability distributions including binomial, Poisson, normal, uniform, and exponential.
- Estimation techniques including point estimates, confidence intervals for means and proportions.
- Hypothesis testing frameworks including stating null and alternative hypotheses, determining test statistics, critical values, and statistical decisions.
- Specific hypothesis tests are described for means when the population standard deviation is known or unknown.
The document is intended as a review of these statistical concepts and includes sample test questions to help with learning.

Discrete and continuous probability models

This document discusses different types of probability distributions used in statistics. There are two main types: continuous and discrete distributions. Continuous distributions are used when variables are measured on a continuous scale, while discrete distributions are used when variables can only take certain values. Some important continuous distributions mentioned are the normal, lognormal, and exponential distributions. Important discrete distributions include the binomial, hypergeometric, and Poisson distributions. Key terms like mean, variance, and standard deviation are also defined. Examples are provided to illustrate how these probability distributions are applied in fields like quality control and reliability engineering.

The-Normal-Distribution, Statics and Pro

statistics and probability pptx

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This document discusses sampling distributions and how to calculate confidence intervals for statistical parameters like the mean and variance of a population based on a sample. It describes key distributions like the normal, chi-square and Student's t distribution. It provides the formulas to determine confidence intervals for the mean when the population variance is known or unknown, and for the variance. The confidence intervals indicate the range within which the true parameter is likely to fall, given a sample estimate and a confidence level like 95%.

Lecture 01 probability distributions

This document provides an outline for a statistical methods course. It covers topics including probability distributions, estimation, hypothesis testing, regression, analysis of variance, and statistical process control. Under probability distributions, it defines key concepts such as random variables, parameters, statistics, and the normal distribution. It also describes properties of the standard normal distribution and how to use the standard normal table to find probabilities and areas under the normal curve.

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The document discusses various measures of dispersion used in statistics including range, standard deviation, variance, mean deviation, quartile deviation, and z-scores. It explains that measures of dispersion quantify how individual values in a dataset deviate from the central tendency or mean. It also covers key probability distributions like the normal and binomial distributions and statistical concepts like skewness and kurtosis.

Ch 8 NORMAL DIST..doc

The document discusses the normal distribution and normal curve. It defines the normal distribution as a theoretical frequency distribution that follows a bell-shaped curve that is symmetrical about the mean. The normal distribution is important in probability and has characteristics like most observations being near the mean and fewer at the extremes. The normal curve is a graphical representation of the normal distribution as a symmetrical, bell-shaped graph with the highest frequency at the mean and lowest on the sides. The document contrasts normal and skewed distributions and discusses kurtosis.

Normal Distribution – Introduction and Properties

In this video you can see Normal Distribution – Introduction and Properties.
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1.1 course notes inferential statistics

This document provides an overview of key concepts in inferential statistics, including distributions, the normal distribution, the central limit theorem, estimators and estimates, confidence intervals, the Student's t-distribution, and formulas for calculating confidence intervals. It defines key terms and concepts, provides examples to illustrate statistical distributions and properties, and outlines the general formulas used to construct confidence intervals for different sampling situations.

The Standard Normal Distribution

The document discusses the standard normal distribution. It defines the standard normal distribution as having a mean of 0, a standard deviation of 1, and a bell-shaped curve. It provides examples of how to find probabilities and z-scores using the standard normal distribution table or calculator. For example, it shows how to find the probability of an event being below or above a given z-score, or between two z-scores. It also shows how to find the z-score corresponding to a given cumulative probability.

Normal distribution

In the likelihood hypothesis, a normal distribution is a sort of ceaseless likelihood conveyance for a genuine esteemed irregular variable. The overall type of its likelihood thickness work is the boundary which is the mean or desire for the circulation, while the boundary is its standard deviation.

biostatistics and research methodology, Normal distribution

Probability distribution , one of its type is Normal distribution

Normal distribution

A normal (Gaussian) distribution, sometimes called Bell curve, is a distribution that occur naturally (eg: Height of people).

Statistics-3 : Statistical Inference - Core

This presentation covers important topics such as
Multiple Independent Random Variables or i.i.d samples.
Expectations or Expected values
T-Distribution
Central Limit Theorem
Asymptotics & Law of Large Numbers
Confidence Intervals

Lecture 9-Normal distribution......... ...pptx

Distribution in research

template.pptx

- Univariate normal distribution describes the distribution of a single random variable and is characterized by its bell-shaped curve. The mean, median, and mode are equal and located at the center. Approximately 68% of the data falls within one standard deviation of the mean.
- Multivariate normal distribution describes the joint distribution of multiple random variables. It generalizes the univariate normal distribution to multiple dimensions. The variables have a consistent relationship that can be modeled as a covariance matrix.
- Examples of data that may follow a normal distribution include heights, test scores, measurement errors, and stock price changes over time. Normal distributions are widely used in statistics

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SY(ECT) PTRP Unit 4 ppts for reference

Normal distribution

Normal distribution

Discrete distributions: Binomial, Poisson & Hypergeometric distributions

Discrete distributions: Binomial, Poisson & Hypergeometric distributions

The Normal Distribution

The Normal Distribution

Review on probability distributions, estimation and hypothesis testing

Review on probability distributions, estimation and hypothesis testing

Discrete and continuous probability models

Discrete and continuous probability models

The-Normal-Distribution, Statics and Pro

The-Normal-Distribution, Statics and Pro

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Ch 8 NORMAL DIST..doc

Ch 8 NORMAL DIST..doc

Normal Distribution – Introduction and Properties

Normal Distribution – Introduction and Properties

1.1 course notes inferential statistics

1.1 course notes inferential statistics

The Standard Normal Distribution

The Standard Normal Distribution

Normal distribution

Normal distribution

biostatistics and research methodology, Normal distribution

biostatistics and research methodology, Normal distribution

Normal distribution

Normal distribution

Statistics-3 : Statistical Inference - Core

Statistics-3 : Statistical Inference - Core

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Lecture 9-Normal distribution......... ...pptx

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template.pptx

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Oracle Database Desupported Features on 23ai (Part B)

Oracle Database Desupported Features on 23ai (Part B)

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Enabling business users to directly query their data sources is a significant advantage for organisations. The majority of enterprise data is housed within databases, requiring extensive procedures that involve intermediary layers for reporting and its related customization. The concept of enabling natural language queries, where a chatbot can interpret user questions into database queries and promptly return results, holds promise for expediting decision-making and enhancing business responsiveness. This approach empowers experienced users to swiftly obtain data-driven insights. The integration of Text-to-SQL and Large Language Model (LLM) capabilities represents a solution to this challenge, offering businesses a powerful tool for query automation. However, security concerns prevent organizations from granting direct database access akin to platforms like OpenAI. To address this limitation, this Paper proposes developing fine-tuned small/medium LLMs tailored to specific domains like retail and supply chain. These models would be trained on domain-specific questions and Queries that answer these questions based on the database table structures to ensure efficacy and security. A pilot study is undertaken to bridge this gap by fine-tuning selected LLMs to handle business-related queries and associated database structures, focusing on sales and supply chain domains. The research endeavours to experiment with zero-shot and fine-tuning techniques to identify the optimal model. Notably, a new dataset is curated for fine-tuning, comprising business-specific questions pertinent to the sales and supply chain sectors. This experimental framework aims to evaluate the readiness of LLMs to meet the demands for business query automation within these specific domains. The study contributes to the progression of natural language query processing and database interaction within the realm of business intelligence applications.

Why_are_we_hypnotizing_ourselves-_ATeggin-1.pdf

I’m excited to finally share my research from last year on the hypnotic effects of mass media and digital platformization. This study explores how our attention is influenced through YouTube’s audio-visual content. Key points:
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- **Focus:** Sound and visual experiences on YouTube.
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- **Findings:** Observations on techniques in attention-based economies and their cognitive impact.
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- 1. Continuous probability distribution Normal distribution:
- 3. Standard normal distribution(Z- distribution) • Let the random variable X has standard normal or Gaussian distribution with mean 𝜇 and standard deviation 𝜎 , • Then the random variable Z is said to have a standard normal distribution if 𝑍 = 𝑋 −𝜇 𝜎 , • the pdf of standard normal distribution is given by: In other words, a normal distribution with mean zero (µ=0) and variance one (σ2=σ=1) is called the standard normal distribution (Z- distribution). Note that Z ~ N(0, 1)
- 7. Application of normal distribution Normal distribution play very important role in statistical theory because of the following reasons i) Most of the distributions occurring in the practice e.g. Binomial, Poisson, Hyper geometric distributions, etc., can be approximated by normal distribution ii) Most of the sampling distributions e.g. Student t, F-distribution, Chi-square distributions etc., tend to normality for large samples. iii) Even if a variable is not normally distributed, it can sometimes be brought to normal form by simple transformation of variable. For example, if the distribution of X is skewed, the distribution of square root of X might come out to be normal. iv) Many of the distributions of sample statistics e.g. the distribution of sample mean, sample variance etc., tend to normality for large samples. v) Normal distribution finds large applications in Statistical Quality Control in industry for setting control limit.
- 11. Applications of the Exponential Distribution: 1. Time between telephone calls 2. Time between machine breakdowns 3. Time between successive job arrivals at a computing center