Let Xn be a sequence of independent random variables. Define the sigma-field F=capn=1^inftysigma(Xn,Xn+1,dots). Suppose Ain F. Then, which of the following statements is more appropriate?

Q55Section III (Statistics)55 of 84

Kolmogorov's 0–1 law for the tail $\sigma$ -field

Let $\{X_n\}$ be a sequence of independent random variables. Define the $\sigma$ -field $F=\bigcap_{n=1}^\infty\sigma(X_n,X_{n+1},\dots)$ . Suppose $A\in F$ . Then, which of the following statements is more appropriate?

Pick an option to check your answer.

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