Student T - OpenAI

I asked Open AI's new chat bot to create a blog about my favorite distribution. So we go.

 Sure, I'd be happy to write a blog about the student's t-distribution! Here is a brief overview of what it is and how it is used:

The student's t-distribution, also known simply as the t-distribution, is a probability distribution that is often used to estimate population parameters when the sample size is small and the population variance is unknown. It is a continuous probability distribution that is symmetric around its mean, and it has heavier tails than the normal distribution, which means that it is more prone to producing extreme values.

One of the key characteristics of the t-distribution is that it depends on a parameter called the degrees of freedom, which is equal to the sample size minus 1. As the degrees of freedom increase, the t-distribution becomes more and more similar to the normal distribution. This property makes the t-distribution useful for testing hypotheses about population means when the sample size is small.

In statistics, the t-distribution is often used in hypothesis testing. For example, if we want to test the hypothesis that the mean of a population is equal to a certain value, we can use the t-distribution to calculate the p-value, which is the probability of observing a test statistic as extreme as the one we observed if the null hypothesis is true. If the p-value is smaller than a certain threshold (usually 0.05), we can reject the null hypothesis and conclude that the population mean is different from the value specified in the null hypothesis.

In summary, the student's t-distribution is a useful tool for statisticians and researchers who want to make inferences about population parameters based on small samples. Its ability to accommodate the uncertainty of the population variance and its flexibility in the number of degrees of freedom make it a valuable tool in many different applications.

Write a blog about the history of creation of student t distribution 

The student's t-distribution, also known simply as the t-distribution, is a probability distribution that is commonly used in statistics to estimate population parameters when the sample size is small and the population variance is unknown. It was first introduced by William Gosset, who was a scientist working for the Guinness brewery in Dublin, Ireland.

Gosset was interested in using statistics to improve the quality and consistency of Guinness's beer. In order to do this, he needed to be able to make inferences about the means of small samples of data. At the time, the only available tools for this were the normal distribution and the chi-squared distribution, but both of these assumptions required the population variance to be known, which was not the case for the data Gosset was working with.

In order to overcome this limitation, Gosset derived a new probability distribution that did not rely on the assumption of known population variance. He published his results under the pseudonym "Student" in 1908 in a paper titled "The Probable Error of a Mean." In this paper, he showed that the distribution of the sample mean of a random sample from a normally distributed population is approximately a t-distribution with n-1 degrees of freedom, where n is the sample size.

Gosset's work was largely overlooked at the time, but it was later rediscovered and popularized by Ronald Fisher, who is considered one of the founders of modern statistics. Fisher recognized the value of Gosset's work and used it to develop a number of statistical tests, including the analysis of variance (ANOVA) and the F-test.

Today, the student's t-distribution is a widely used tool in statistics, and it continues to be an important part of the statistical toolkit for researchers and analysts who need to make inferences about population parameters based on small samples. It is a testament to Gosset's ingenuity and insight that his work continues to be relevant and useful more than a century after it was first published.

Great but can you add more about why it's student t rather than named after gosset

Certainly! The student's t-distribution is so named because it was first published by William Gosset under the pseudonym "Student." Gosset was a scientist working for the Guinness brewery in Dublin, Ireland, and he published his work in 1908 in a paper titled "The Probable Error of a Mean."

Gosset chose to publish under a pseudonym because Guinness had a policy at the time that prohibited their employees from publishing scientific work. Gosset was able to continue his research and publish his findings without violating this policy by using the pseudonym "Student."

Despite Gosset's efforts to remain anonymous, his identity was eventually revealed, and he is now credited with the development of the student's t-distribution. However, the name "student's t-distribution" has stuck, and it continues to be used to this day to refer to this important probability distribution in statistics.

This is quite cool but makes me nervous that it could create wikipedia bubbles. That only agree with the political view of the reader. I have seen other people use this and the AI made up sources and brought back wrong maths answers. I can see this replacing google. I like knowing the history of Gosset. So instead of seeing created article; I got this AI to create one. Amazon had to stop using there AI for reading CV as rarely put forward Women's CV. AI isn't control by anyone and see correlation and causation as the same thing. Great example is number of movies Nicolas Cage appears in each year and the number of people who drown in their swimming pools. There is a correlation but no causation. I will let the bot have last word