In recent times, expectation wiktionary the free dictionary has become increasingly relevant in various contexts. 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 Calculate expectation of a geometric random variable.
2 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. Moreover, and (b) the total expectation theorem. Difference between logarithm of an expectation value and expectation ....
statistics - What is the expectation of $ X^2$ where $ X$ is .... What is the expectation of $ X^2$ where $ X$ is distributed normally? Ask Question Asked 13 years, 10 months ago Modified 10 years, 5 months ago
probability - Infinite expected value of a random variable .... Part of it might be because of the word "expectation." In common usage, when we expect something to happen, we think it's more likely to happen than not. But in probability, that's clearly not the case, because we're taking a weighted average of possible outcomes, and the weighted average itself might be an unlikely, or even impossible outcome. Interchange of expected value and summation - Mathematics Stack Exchange.
Equally important, the expectation operator is linear. This means that you can change the order of taking expectations and taking sums. In both of the formulas that you state, this is exactly what is done: on the left-hand sides, the sum is taken first and then the expectation, on the right-hand sides the expectation is taken first and then the sum. Both formulas are correct .
Expected value of an expected value - Mathematics Stack Exchange. You'll need to complete a few actions and gain 15 reputation points before being able to upvote. Upvoting indicates when questions and answers are useful.
What's reputation and how do I get it? Instead, you can save this post to reference later. Additionally, expectation - Proof for Mean of Geometric Distribution - Mathematics .... How did you reformulate the density function into an arithmetico-geometric series?
Otherwise, the result for the sum of geometric series is very well known and it is not unusual to transform a mathematical expression into another, familiar one via simple operations to make the solution apparent. It doesn't mean your approach is wrong, but you might have needed to check Wikipedia to get the result. Expectation of an exponential function - Mathematics Stack Exchange. Why is the expectation of an exponential function: $$\mathbb {E} [\exp (A x)] = \exp ( (1/2) A^2)\,?$$ I am struggling to find references that shows this, can anyone help me please?
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