Skip to main content
MathOverflow

Return to Question

added 3 characters in body
Source Link
John Wong
John Wong
  • 773
  • 6
  • 11

Let $X_1,X_2,...$ be iid random variable with mean zero. If $X_1$ has second moment thatthen by the CLT we have $P(X_1+X_2+...+X_n\geq 0)\rightarrow \frac{1}{2}$, as $n$ goes to infinity. I am curious about thatwhether does this hold without the second moment assumption? I think this might be a well studied problem. Could anyone provide an answer or reference to me? Many thank!

Let $X_1,X_2,...$ be iid random variable with mean zero. If $X_1$ has second moment that by the CLT we have $P(X_1+X_2+...+X_n\geq 0)\rightarrow \frac{1}{2}$, as $n$ goes to infinity. I am curious about that does this hold without the second moment assumption? I think this might be a well studied problem. Could anyone provide an answer or reference to me? Many thank!

Let $X_1,X_2,...$ be iid random variable with mean zero. If $X_1$ has second moment then by the CLT we have $P(X_1+X_2+...+X_n\geq 0)\rightarrow \frac{1}{2}$, as $n$ goes to infinity. I am curious about whether does this hold without the second moment assumption? I think this might be a well studied problem. Could anyone provide an answer or reference to me? Many thank!

Source Link
John Wong
John Wong
  • 773
  • 6
  • 11

probability of IID sum being positive

Let $X_1,X_2,...$ be iid random variable with mean zero. If $X_1$ has second moment that by the CLT we have $P(X_1+X_2+...+X_n\geq 0)\rightarrow \frac{1}{2}$, as $n$ goes to infinity. I am curious about that does this hold without the second moment assumption? I think this might be a well studied problem. Could anyone provide an answer or reference to me? Many thank!