The link between the variance of $\bar { Y }$ and the probability that $\bar { Y }$ is within $\pm \delta \text { of } \mu _ { Y }$ is provided by
A) Slutsky's theorem.
B) the Central Limit Theorem.
C) the Law of Large Numbers.
D) Chebychev's inequality.

Question

The link between the variance of $\bar { Y }$  and the probability that $\bar { Y }$  is within $\pm \delta \text { of } \mu _ { Y }$ is provided by
A) Slutsky's theorem.
B) the Central Limit Theorem.
C) the Law of Large Numbers.
D) Chebychev's inequality.

Quizplus · Accepted Answer

Chebychev's inequality provides a bound on the probability that a random variable deviates from its mean by more than a certain amount, which directly relates the variance to the probability of $\bar{Y}$ being within $\pm \delta$ of $\mu_Y$.

The Link Between the Variance Of Yˉ\bar { Y }Yˉ And the Probability That

The Link Between the Variance Of $\bar { Y }$ And the Probability That