Lecture

Normal Distribution: Characteristics and Examples

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In course

MICRO-110: Probability & statistics for engineers

This course covers the basics of probability and statistical techniques for engineers, including major probability concepts, data analysis, and statistical inference.

Description

This lecture covers the characteristics of the normal distribution, including its symmetry, bell-shaped curve, and the rule for the normal density function. It explains the importance of the normal distribution in the central limit effect and robustness to assumption of normality. Examples of normality in different scenarios are provided, such as the height of male students and the effect of sample size on approaching normal distribution. The lecture also discusses z-scores, treatment examples like heat treating a 3D printed metal part, and the concept of repeated sampling. Special cases like random sampling from a normal distribution and the binomial distribution are explored, along with the probability associated with it.

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Instructor

Vivek Subramanian

Teaching & PhD PhD Students Giovanni Ruffolo, Giada Romano, Sanjay Manoharan, Kyle Haas, Claude Dahan, Biruktait Ayele Lemecho, Yagmur Ceren Alatas, Tugçe Delipinar Past EPFL PhD Students Amin Hodaei, Mustafa Mohieldin Fadlelmula Fadlelseed Past EPFL PhD Students as codirector Mohammad Jafarpour Courses Organic and printed electronics MICRO-505 This course addresses the implementation of organic and printed electronics technologies using large area manufacturing techniques. It will provide

Official source

Ontological neighbourhood

Statistics

Statistical inference: Mathematical statistics

Data collection: Statistical sampling

Related concepts (31)

Sampling (statistics)

In statistics, quality assurance, and survey methodology, sampling is the selection of a subset or a statistical sample (termed sample for short) of individuals from within a statistical population to estimate characteristics of the whole population. Statisticians attempt to collect samples that are representative of the population. Sampling has lower costs and faster data collection compared to recording data from the entire population, and thus, it can provide insights in cases where it is infeasible to measure an entire population.

Simple random sample

In statistics, a simple random sample (or SRS) is a subset of individuals (a sample) chosen from a larger set (a population) in which a subset of individuals are chosen randomly, all with the same probability. It is a process of selecting a sample in a random way. In SRS, each subset of k individuals has the same probability of being chosen for the sample as any other subset of k individuals. A simple random sample is an unbiased sampling technique. Simple random sampling is a basic type of sampling and can be a component of other more complex sampling methods.

Stratified sampling

In statistics, stratified sampling is a method of sampling from a population which can be partitioned into subpopulations. In statistical surveys, when subpopulations within an overall population vary, it could be advantageous to sample each subpopulation (stratum) independently. Stratification is the process of dividing members of the population into homogeneous subgroups before sampling. The strata should define a partition of the population.

Skew normal distribution

In probability theory and statistics, the skew normal distribution is a continuous probability distribution that generalises the normal distribution to allow for non-zero skewness. Let denote the standard normal probability density function with the cumulative distribution function given by where "erf" is the error function. Then the probability density function (pdf) of the skew-normal distribution with parameter is given by This distribution was first introduced by O'Hagan and Leonard (1976).

Multivariate normal distribution

In probability theory and statistics, the multivariate normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization of the one-dimensional (univariate) normal distribution to higher dimensions. One definition is that a random vector is said to be k-variate normally distributed if every linear combination of its k components has a univariate normal distribution. Its importance derives mainly from the multivariate central limit theorem.

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