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- The expectation of an expectation - Mathematics Stack Exchange
This may seem trivial but just to confirm, as the expected value is a constant, this implies that the expectation of an expectation is just itself It would be useful to know if this assumption is correct or if any subtleties cause this not to be true i e $ \mathbb{E[\mathbb{E[x]}]}=\mathbb{E[x]} $
- Calculate expectation of a geometric random variable
A clever solution to find the expected value of a geometric r v is those employed in this video lecture of the MITx course "Introduction to Probability: Part 1 - The Fundamentals" (by the way, an extremely enjoyable course) and based on (a) the memoryless property of the geometric r v and (b) the total expectation theorem
- What is the difference between Average and Expected value?
The distinction is subtle but important: The average value is a statistical generalization of multiple occurrences of an event (such as the mean time you waited at the checkout the last 10 times you went shopping, or indeed the mean time you will wait at the checkout the next 10 times you go shopping)
- probability - measure-theoretic definition of expectation - Mathematics . . .
What is the intuition behind conditional expectation in a measure-theoretic treatment of probability? 6 Reconciling measure-theoretic definition of expectation versus expectation defined in elementary probability
- Expected value of a Gaussian - Mathematics Stack Exchange
$\begingroup$ You're very welcome And you got it! The integral over $(-\infty, \infty)$ of a pdf results in 1 (which intuitively makes perfect sense, since when you integrate a pdf over an interval, you are calculating the probability that the random variable lands in that interval, so when you integrate a pdf over $(-\infty, \infty)$ you are calculating the probability that the random
- Expected value of an expected value - Mathematics Stack Exchange
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- Newest conditional-expectation Questions - Mathematics Stack Exchange
For every question related to the concept of conditional expectation of a random variable with respect to a $\sigma$-algebra It should be used with the tag (probability-theory) or (probability), and other ones if needed
- expectation - What is the expected value of a probability density . . .
Random events have two characteristics: a value and a probability It's clear in the discrete case; a normal die has a 1 6 probability of rolling each of one through six
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