0
$\begingroup$

enter image description here The question is based on weak law of large numbers.So the given pdf here is a gamma distribution with population mean=2.The answer given to the question is 0.Shouldn't be the probability 1 according to weak law of large numbers!?

enter image description here

$\endgroup$
2
$\begingroup$

$\bar{X}_n$ is a continuous random variable, hence for all $n>0$, $P(\bar{X}_n=2)=0$

Hence, $\lim_{n \to \infty}P(\bar{X}_n = 2) =0$.

Weak law of large number says that $\lim_{n \to \infty} P(|\bar{X}_n -2| \leq \epsilon) =1$.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.