Samples population and distribution Flashcards
What is a population
1 - A population can be an actually existing (and therefore finite) set of objects, such as all people currently living in the UK, or every printed mathematics textbook worldwide. The number of members in this population is called the population size and often denoted by π.
2 - A population can also be constructed hypothetically, by extrapolating from a finitely large to an infinitely large set of objects, such as an infinite number of dice rolls or coin tosses.
3 - A population can be a completely abstract object that is described mathemati- cally, such as the population of numbers drawn from the exponential distribution with parameter π = 2.
What is a sample?
A sample is a subset of a population, selected from the population through a well-defined process, such as random selection, or non-random selection based on some criterion. The purpose of a sample is usually to learn about the properties of the population. The process of selecting a sample is called sampling, and the number of members in the sample is called the sample size and is often denoted by π.
What is a sample statistic?q
a scalar quantity - βs(x1,x2,x3β¦xn)β
What is a sample moment?
The π-th sample moment πβ²π of a sample π₯ = {π₯1, β¦ , π₯π} is defined as
(1/n)*SUM(Xi^k)
What is the sample mean in terms of moments
The first sample moment
What does the sample mean describe
The number that is closest to all other numbers in the sample.
Itβs the sum of squared distances
What is the kith central sample moment
(1/n)*SUM(Xi^x)^k
What is the sample variance in terms of moments
The second sample moment
What is the Kβth order statistic?
The kβth smallest value in a sample
what is the P-quantile of a sample?
a value that is not exceeded by a proportion P of the data, and is exceeded by 1-p proportion of the data
How can we describe the Skew of a sample?
Pearsons moment coefficient
(The third central moment)/SD^3
Yules coefficient
