# Bound on the Expectation of the ratio of two random variables not necessarily independent

by Avah   Last Updated September 11, 2019 19:20 PM

Suppose we have two sequences of random variables $$\{X_n\}$$ and $$\{Y_n\}$$ with $$X_n \ge Y_n \ge 1$$ such that $$\mathbb{E}[X_n - Y_n] < c$$ (for some constant $$c$$).

Is it possible $$\mathbb{E}[X_n/Y_n]$$ is unbounded?

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