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


$\bar{X}_n$ 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 $\lim_{n \to \infty} P(|\bar{X}_n -2| \leq \epsilon) =1$.


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