Let X1,X2,…Xn be a random sample from the density f(x;(θ), where θ may be vector. If the conditional distribution of X1,X2,…Xn given S=s does not depend on θ for any value of s of S, then statistic is called?

Related Mcqs:

1. Let X1,X2,……,Xn be a random sample from a density,,,, f(x ι θ) where θ is a value of the random variable Θwith known density gΘ(θ) Then the estimator ∏(θ) with…/ respect to the prior gΘ(θ) is define as_________________E[∏(θ)ιX1,X2,…..,Xn] is called?

   A. Posterior Bay’s estimator
   B. Minimax estimator
   C. Bay’s estimator
   D. Sufficient estimator

2. Let X1,X2,……,Xn be a random sample from a density,,,, f(x ι θ) where θ is a value of the random variable Θwith known density gΘ(θ) Then the estimator ∏(θ) with…/ respect to the prior gΘ(θ) is define as______________E[∏(θ)ιX1,X2,…..,Xn] is called?

   A. Posterior Bay’s estimator
   B. Minimax estimator
   C. Bay’s estimator
   D. Sufficient estimator

3. Let Z1,Z2,….Zn be independent and identically distributedrandom variable, satisfying E[ι Zt ι]<∞. Let N be an integer valued random variable whose value n depends only on the values of the first n Z¡'s. Suppose E(N)< ∞, then E(Z1,Z2,….Zn)=E(N)E(Z) is called ?

   A. Independence Equation
   B. Sequential Probability Likelihood Equation
   C. Neyman Pearson Lemma
   D. Wald’s Equation

4. If the conditional distribution of X1,X2,…..Xn given S=s, does not depends on θ, for any value of S=s the statistics S=s(X1,X2,…..Xn) is called______________?

   A. Unbiased
   B. Sufficient
   C. Consistent
   D. Efficient

5. If the sampled population has a normal distribution, when is the sampling distribution of the sample mean X also a normal distribution ?

   A. Only when the sample size is at least 100.
   B. Only when the sample size is smaller than 30
   C. Always
   D. Only when the sample size is at least 30.

6. Random samples of size 17 are from a population that has 200 elements, a mean of 36, and a standard deviation of 8. which of the following best describes the from of the sampling distribution of the sample mean for this situation ?

   A. Approximately normal because the sample size is small relative to the population size
   B. Approximately normal because of the central limit theorem
   C. Exactly
   D. None of these alternatives is correct

7. Normal distribution is a probability distribution of _____ random variable?

   A. Continuous
   B. Constant
   C. Discrete
   D. Normal

8. A_______ is the specific value of the statistic used to estimate the population parameter?

   A. Point estimator
   B. C.I.
   C. Estimator
   D. None of these

9. The critical value of a test statistic is determined from_____________?

   A. The sampling distribution of the statistics assuming Null Hypothesis
   B. calculations based on many actual repetitions of the same Experiment
   C. The sampling distribution of the statistic assuming Alternative Hypothesis.
   D. Non of these

10. For a population with any distribution, the form of the sampling distribution of the sample mean is_____________?

    A. Sometimes normal for all sample sizes
    B. Sometimes normal for large sample sizes
    C. Always normal for all sample sizes
    D. Always normal for large sample sizes