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Results tagged with conditional-expectation
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user 181388
A conditional expectation is the expectation of a random variable, given information on another variable or variables (mostly, by specifying their value).
2
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For random variable $Z=\max_i X_i$, can we bound $\mathbb{E}(Z|Z>\tau)$ with $\mathbb{E}(Z)$
Let $X_1,…,X_n$ be independent, but not necessarily identical, non-negative random variables. Let $Z=\max_i(X_i)$. Fix a real $\tau > 0$. Is there a way to lower bound $$\mathbb{E}(Z|Z>\tau) > c \math …
- 243
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Ratio between expectation of maximum of $n$ and $n-1$ IID random variables
Let $X_1, ..., X_n$ be iid random variables. Define $Z_n = \max(X_1, ..., X_n)$. Can we lower bound
$$\mathbb{E}[Z_{n-1}] \geq (1-f(n))\mathbb{E}[Z_n]$$
Using some $f(n)$. I am mainly interested in sm …
- 243