Questions tagged [expected-value]
The expected value of a random variable is a weighted average of all possible values a random variable can take on, with the weights equal to the probability of taking on that value.
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Find expected value using CDF
I'm trying to solve the following problem:
Let $X$ have the CDF $F(x) = 1 - x^{-\alpha}, x\ge1$.
Find $E(X)$ for those values of $\alpha$ for which $E(X)$ exists.
How can I determine which values of ...
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Why is expectation the same as the arithmetic mean?
Today I came across a new topic called the Mathematical Expectation. The book I am following says, expectation is the arithmetic mean of random variable coming from any probability distribution. But, ...
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Deriving Bellman's Equation in Reinforcement Learning
I see the following equation in "In Reinforcement Learning. An Introduction", but don't quite follow the step I have highlighted in blue below. How exactly is this step derived?
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Taking the expectation of Taylor series (especially the remainder)
My question concerns trying to justify a widely-used method, namely taking the expected value of Taylor Series. Assume we have a random variable $X$ with positive mean $\mu$ and variance $\sigma^2$. ...
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What is the difference between finite and infinite variance
What is the difference between finite and infinite variance ? My stats knowledge is rather basic; Wikipedia / Google wasn't much help here.
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Brain-teaser: What is the expected length of an iid sequence that is monotonically increasing when drawn from a uniform [0,1] distribution?
This is an interview question for a quantitative analyst position, reported here. Suppose we are drawing from a uniform $[0,1]$ distribution and the draws are iid, what is the expected length of a ...
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MSE decomposition to Variance and Bias Squared
In showing that MSE can be decomposed into variance plus the square of Bias, the proof in Wikipedia has a step, highlighted in the picture. How does this work? How is the expectation pushed in to the ...
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Why is the expected value named so?
I understand how we get 3.5 as the expected value for rolling a fair 6-sided die.
But intuitively, I can expect each face with equal chance of 1/6.
So shouldn't the expected value of rolling a die ...
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Why not report the mean of a bootstrap distribution?
When one bootstraps a parameter to get the standard error we get a distribution of the parameter. Why don't we use the mean of that distribution as a result or estimate for the parameter we are trying ...
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Expected value of a natural logarithm
I know $E(aX+b) = aE(X)+b$ with $a,b $ constants, so given $E(X)$, it's easy to solve. I also know that you can't apply that when its a nonlinear function, like in this case $E(1/X) \neq 1/E(X)$, and ...
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Can somebody offer an example of a unimodal distribution which has a skewness of zero but which is not symmetrical?
In May 2010 Wikipedia user Mcorazao added a sentence to the skewness article that "A zero value indicates that the values are relatively evenly distributed on both sides of the mean, typically but not ...
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I've heard that ratios or inverses of random variables often are problematic, in not having expectations. Why is that?
The title is the question. I am told that ratios and inverses of random variables often are problematic. What is meant is that expectation often do not exist. Is there a simple, general explication of ...
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Why should the frequency of heads in a coin toss converge to anything at all?
Suppose we have any kind of coin. Why should the relative frequency of getting a heads converge to any value at all?
One answer is that this is simply what we empirically observe this to be the case, ...
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Sample two numbers from 1 to 10; maximize the expected product
Assume you sample two numbers, randomly drawn from 1 to 10; you could choose two strategies: 1) pick with replacement and 2) pick without replacement. Which strategy would you prefer to maximize the ...
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Why maximum likelihood and not expected likelihood?
Why is it so common to obtain maximum likelihood estimates of parameters, but you virtually never hear about expected likelihood parameter estimates (i.e., based on the expected value rather than the ...
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