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1. The function x ↦ 1 / x is only convex on the domains (0, + ∞) or ( − ∞, 0). Therefore, the inequality E[1 / X] ≥ 1 / E[X] is only valid if P(X > 0) = 1 or P(X < 0) = 1. For example, if P(X = 1) = 2 / 3 and P(X = − 1) = 1 / 3, then E[1 / X] = 1 / 2, while 1 / E[X] = 2. – Mike Earnest. Jan 17, 2022 at 18:42.
19 paź 2019 · You don't have to use the values of X X at all. This follows from the fact that X − b X − b and b − X b − X have the same distribution (as you can verify from the definition of symmetry). If two random variables have the same distribution the they have the same mean (assuming that the mean exists).
10 cze 2018 · Suppose I have a line segment of length $L$. I now select two points at random along the segment. What is the expected value of the distance between the two points, and why?
27 lut 2015 · The calculation of E[X − 1] when X is a Gamma random variable with order parameter n and rate parameter λ requires recognition of the density of another Gamma random variable (with order parameter n − 1 and rate parameter λ) in the integral given by the law of the unconscious statistician for E[X − 1]. We have.
In probability theory, the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, expectation value, or first moment) is a generalization of the weighted average.
As in Problem 1, the expected value of each of the pieces - due to the Symmetry Principle - is $\displaystyle\frac{1}{3}.$ However, if we talk of the expected values of the shortest, middle, and the longest segments, then all three numbers are different.
In probability theory, an expected value is the theoretical mean value of a numerical experiment over many repetitions of the experiment. Expected value is a measure of central tendency; a value for which the results will tend to.
