CA Foundation Exam > CA Foundation Questions > A unbiased estimator:a)Has the smallest varia...
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A unbiased estimator:
- a)Has the smallest variance among all estimator:
- b)Is always the best estimator.
- c)Has an expected value equal to the true parameter value.
- d)Always generates the true value of the parameter.
Correct answer is option 'C'. Can you explain this answer?
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A unbiased estimator:a)Has the smallest variance among all estimator:b...
Explanation:
Unbiased Estimator Definition:
An unbiased estimator is a statistic that, on average, gives the true value of the parameter it is estimating.
Expected Value of an Estimator:
The expected value of an estimator is the average value the estimator would give if we were to repeat the estimation process over and over again.
True Parameter Value:
The true parameter value is the actual value of the population parameter being estimated.
Explanation of Option 'C':
Option 'C' states that an unbiased estimator has an expected value equal to the true parameter value. This means that when we calculate the average value of the estimator over multiple samples, it will be equal to the true value of the parameter we are trying to estimate.
This property makes unbiased estimators desirable because it means that, on average, they provide accurate estimates of the population parameter. This is important in statistics because we want our estimators to be as close to the true value as possible.
Therefore, option 'C' is the correct answer because it accurately describes the key characteristic of an unbiased estimator.
Unbiased Estimator Definition:
An unbiased estimator is a statistic that, on average, gives the true value of the parameter it is estimating.
Expected Value of an Estimator:
The expected value of an estimator is the average value the estimator would give if we were to repeat the estimation process over and over again.
True Parameter Value:
The true parameter value is the actual value of the population parameter being estimated.
Explanation of Option 'C':
Option 'C' states that an unbiased estimator has an expected value equal to the true parameter value. This means that when we calculate the average value of the estimator over multiple samples, it will be equal to the true value of the parameter we are trying to estimate.
This property makes unbiased estimators desirable because it means that, on average, they provide accurate estimates of the population parameter. This is important in statistics because we want our estimators to be as close to the true value as possible.
Therefore, option 'C' is the correct answer because it accurately describes the key characteristic of an unbiased estimator.
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A unbiased estimator:a)Has the smallest variance among all estimator:b)Is always the best estimator.c)Has an expected value equal to the true parameter value.d)Always generates the true value of the parameter.Correct answer is option 'C'. Can you explain this answer?
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