For real numbers \( a, b \), find the following limit.
\[
\lim_{n \to \infty} n \left( 1 – \frac{a}{n} – \frac{b \log (n+1)}{n} \right)^n.
\]
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Daily Archives: October 4, 2013
Solution: 2013-15 Bounded random variable
Let \( x, y \) be real numbers satisfying \( y \geq x^2 + 1 \). Prove that there exists a bounded random variable \( Z \) such that
\[
E[Z] = 0, E[Z^2] = 1, E[Z^3] = x, E[Z^4] = y.
\]
Here, \( E \) denotes the expectation.
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Other solutions are submitted by 박민재(+3), 이주호(+3), 장경석(+3), 진우영(+3). Thank you for your participation.
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