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What is the difference between random sampling and dependent sampling?
Are sample mean and sample variance independent random variables?
Is n a random variable?
What are the characteristics of a random variable?
Sep 2, 2020 · For example, the term “dependent samples” means the same thing as dependent groups. Independent Samples vs. Dependent Samples Hypothesis tests and statistical modeling that compare groups have assumptions about the nature of those groups.
Let \(X_1,X_2,\ldots, X_n\) be a random sample of size \(n\) from a distribution (population) with mean \(\mu\) and variance \(\sigma^2\). What is the mean, that is, the expected value, of the sample mean \(\bar{X}\)?
Mar 26, 2023 · The sample mean is a random variable; as such it is written \(\bar{X}\), and \(\bar{x}\) stands for individual values it takes. As a random variable the sample mean has a probability distribution, a mean \(μ_{\bar{X}}\), and a standard deviation \(σ_{\bar{X}}\).
Apr 9, 2022 · A simple random sample is taken from the population and pairs of measurement are collected. This is also called related sampling or matched pair design. Dependent sampling actually reduces to a one population model of differences. X¯¯¯¯d X ¯ d is the sample mean of the differences of each pair.
Mar 27, 2023 · If a random sample of size \(100\) is taken from the population, what is the probability that the sample mean will be between \(2.51\) and \(2.71\)? Solution The sample mean \(\overline{X}\) has mean \(\mu _{\overline{X}}=\mu =2.61\) and standard deviation \(\sigma _{\overline{X}}=\dfrac{\sigma }{\sqrt{n}}=\dfrac{0.5}{10}=0.05\), so
In Example 2, both the random variables are dependent . Thus the mean of the sum of a student’s critical reading and mathematics scores must be different from just the sum of the expected value of first RV and the second RV. But the answer says the mean is equal to the sum of the mean of the 2 RV, even though they are independent.
Oct 28, 2019 · This means that each of the observations is the square of an independent standard normal random variable. As such, their values are all positive. To see why the sample mean and sample variance are now dependent, suppose that the sample mean is small, and close to zero.
