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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 $E[(X+Y)^2]$ given $E(X^2)=3$ $E(Y^2)=4$ and $E(XY) = 2$

I know this is an easy question but I'm having problems solving it I sorta thought that you'd get $E(X^2) + 2E(XY) + E(Y^2)$ and that'd add up to: $3+4+4=11$ but my answer isn't correct. I'm guessing ...
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Does this expectation inequality holds?

Let $X\in L_p(P), p>1$. Is the following result true? $$E[\lvert X\rvert I(\lvert X\rvert>C)]\leq C^{1-p}E\lvert X\rvert^p.$$ where $C>0$. It can be found in the proof of Corollary A.1 (...
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Chi-square Goodness of fit with specific expected values

Let's say I have the following summary data/observed counts. ...
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