It’s denoted E(Y). It’s also called the often denoted as µ. population mean, It’s what we do know in this example. not A is typically denoted (read "y-bar"). sample mean It’s calculated from a sample y1, y2, ... , yn of values of Y by the familiar formula = (y1+ y2+ ... + yn)/n. The sample mean is an of the population mean µ, estimate but they are usually the same. not Confusing them is a common mistake. Note the articles: "the population mean" but "a sample mean". is only one mean associated with the population random variable Y. However, a mean depends on the sample sample chosen. Since there are many possible samples, there are many possible sample means. Illustration: https://istats.shinyapps.io/sampdist_cont/ (Use and explore.) “Bell-shaped” Putting this in a more general framework: A is a constant associated with a population. parameter In our example: The population mean µ is a parameter.
It’s denoted E(Y). It’s also called the population mean, often denoted as µ. It’s what we do not know in this example. A sample mean is typically denoted (read "y-bar"). It’s calculated from a sample y1, y2, ... , yn of values of Y by the familiar formula = (y1+ y2+ ... + yn)/n. The sample mean is an estimate of the population mean µ, but they are usually not the same. Confusing them is a common mistake. Note the articles: "the population mean" but "a sample mean". is only one population mean associated with the random variable Y. However, a sample mean depends on the sample chosen. Since there are many possible samples, there are many possible sample means. Illustration: https://istats.shinyapps.io/sampdist_cont/ (Use “Bell-shaped” and explore.) Putting this in a more general framework: A parameter is a constant associated with a population. In our example: The population mean µ is a parameter.