Question

What is the justification for $\lim_{m \rightarrow \infty} \frac 1 m \sum_{i = 1}^m X_i= \int_{-\infty}^{\infty} x f(x) \, dx = \operatorname EX$

score 86 · Answer 1 · 2018-05-23 22:45:03

86

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What is the justification for $\lim_{m \rightarrow \infty} \frac 1 m \sum_{i = 1}^m X_i= \int_{-\infty}^{\infty} x f(x) \, dx = \operatorname EX$

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278

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List Question

What is the justification for $\lim_{m \rightarrow \infty} \frac 1 m \sum_{i = 1}^m X_i= \int_{-\infty}^{\infty} x f(x) \, dx = \operatorname EX$

How many sticker packets do I need to complete an album?

the expectation notation

given random variable $X$ and function $g(x)$ , can I calculate $E(g(X))$ in a simple way?

Coupon collector expectation using definition

Convergence of Truncated Expectation of Order Statistics $E[Y_{k:N}|Y_{k:N}>v]\rightarrow v$

Hitting time of 2D markov chain

Understanding the formula for variance

Conditional Expectation Greater than Constant

If $\left< e^{-x}\right>=1$ then $\left<x\right>\ge 0$.

A peculiar linear programming: random variables and limits

Calculate Difference between Expectation and Conditional Expectation

How Can I calculate mean value of Random Variable

Expected value of $\sin(X)$, where $X$ is a Cantor random variable

Expectation of number of equal points in tennis game

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