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Why the sample variance is an unbiased estimator of the population variance?
The sample variance is considered an unbiased estimator of the population variance because it corrects for the bias introduced by estimating the population variance from a sample. When calculating the sample variance, we use ( n-1 ) (where ( n ) is the sample size) instead of ( n ) in the denominator, which compensates for the degree of freedom lost when estimating the population mean from the sample. This adjustment ensures that the expected value of the sample variance equals the true population variance, making it an unbiased estimator.
What is the mean and variance of throwing unbiased dice?
When throwing a single unbiased six-sided die, the mean (expected value) is calculated as the average of the outcomes: (1 + 2 + 3 + 4 + 5 + 6) / 6 = 3.5. The variance measures the spread of the outcomes around the mean, which is calculated as the average of the squared deviations from the mean: the variance for a single die is 2.9167 (or 35/12). For multiple dice, the mean is the number of dice times 3.5, and the variance is the number of dice times 2.9167.
What does n-1 indicate in a calculation for variance?
The n-1 indicates that the calculation is being expanded from a sample of a population to the entire population. Bessel's correction(the use of n − 1 instead of n in the formula) is where n is the number of observations in a sample: it corrects the bias in the estimation of the population variance, and some (but not all) of the bias in the estimation of the population standard deviation. That is, when estimating the population variance and standard deviation from a sample when the population mean is unknown, the sample variance is a biased estimator of the population variance, and systematically underestimates it.
What difference between a favorable variance and an unfavorable variance?
Favourable variance is that variance which is good for business while unfavourable variance is bad for business
What is objectivity in statistics?
the use of random sampling that results in an unbiased conclusion.
What is the proof that the sample variance is an unbiased estimator?
The proof that the sample variance is an unbiased estimator involves showing that, on average, the sample variance accurately estimates the true variance of the population from which the sample was drawn. This is achieved by demonstrating that the expected value of the sample variance equals the population variance, making it an unbiased estimator.
Is sample variance unbiased estimator of population variance?
No, it is biased.
Show that in simple random sampling the sample variance is an unbiased estimator of population variance?
It is a biased estimator. S.R.S leads to a biased sample variance but i.i.d random sampling leads to a unbiased sample variance.
What is the proof that demonstrates the unbiased estimator of variance?
The proof that demonstrates the unbiased estimator of variance involves showing that the expected value of the estimator equals the true variance of the population. This is typically done through mathematical calculations and statistical principles to ensure that the estimator provides an accurate and unbiased estimate of the variance.
Is there a proof that demonstrates the unbiasedness of the sample variance?
Yes, there is a mathematical proof that demonstrates the unbiasedness of the sample variance. This proof shows that the expected value of the sample variance is equal to the population variance, making it an unbiased estimator.
What does it mean to say that the sample variance provides an unbiased estimate of the population variance?
It means you can take a measure of the variance of the sample and expect that result to be consistent for the entire population, and the sample is a valid representation for/of the population and does not influence that measure of the population.
How can I calculate portfolio variance in Excel?
To calculate portfolio variance in Excel, you can use the formula SUMPRODUCT(COVARIANCE.S(array1,array2),array1,array2), where array1 and array2 are the returns of the individual assets in your portfolio. This formula takes into account the covariance between the assets and their individual variances to calculate the overall portfolio variance.
Standard deviation considered a crude measure of variance?
No. Well not exactly. The square of the standard deviation of a sample, when squared (s2) is an unbiased estimate of the variance of the population. I would not call it crude, but just an estimate. An estimate is an approximate value of the parameter of the population you would like to know (estimand) which in this case is the variance.
What is the formula for calculating variance and standard deviation?
b-a/6
What is rao?
Rao is the guy who helped deelope th Rao Blackwell Theorem in 1945 it is the unique minimum variance unbiased estamator of its expected value
What has the author James D Malley written?
James D. Malley has written: 'Statistical applications of Jordan algebras' -- subject(s): Mathematical statistics, Jordan algebras 'Optimal unbiased estimation of variance components' -- subject(s): Estimation theory, Analysis of variance
In the presence of heteroscedasticity OLS estimators are biased as well as inefficient?
They are still unbiased however they are inefficient since the variances are no longer constant. They are no longer the "best" estimators as they do not have minimum variance
