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 and (b) the total expectation theorem
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 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 a Binomial distribution? - Mathematics Stack Exchange As far as resources go, I remember learning things like this variously from "Art and Craft of Problem Solving", Art of Problem Solving's "Introduction to" and "Intermediate Counting and Probability" Depending on your goals, there may better sources for this stuff For instance, the Wikipedia page on binomial coefficients is moderately comprehensive