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 ?

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. Discrete random variable is real valued function defined on a ___________ sample space?

   A. Discrete
   B. Variable
   C. Scale
   D. Non of these

4. 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?

   A. Minimal sufficient statistic
   B. Sufficient statistic
   C. Efficient
   D. Minimax statistics

5. A random variable is that whose value is determined by the outcome of _________________?

   A. Trial
   B. event
   C. Experiment
   D. Random experiment

6. A continuous random variable which can assume all possible values on scale in a given _______________?

   A. Interval
   B. Point
   C. Time
   D. Sample space

7. A binomial random variable can assume values from _________ to n?

   A. 6
   B. 3
   C. 2
   D. 0

8. A function probability that a random variable of x has a value less than is called _____________?

   A. Random function
   B. Distribution function
   C. Continuous function
   D. probability function

9. For two independent random variables X & Y, Var (x ± y)=___________?

   A. Var(X) + Var (Y)
   B. Var(X) – Var (Y)
   C. Var (X)±
   D. Zero

10. A random variable may be _____________?

    A. fixed
    B. continuous
    C. discrete
    D. discrete or continuous