Raja99
what is the expected value of x^2 in mathematical form?
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Raja99
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in a simplified form
lgbasallote
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what do you mean?
ParthKohli
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\(x \times x\) I think that's what you mean.
Raja99
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yeah
lgbasallote
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mathematical form?
ParthKohli
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Hmm. Similarly:
\( \color{Black}{\Rightarrow x^3 = x \times x\times x}\)
\( \color{Black}{\Rightarrow x^4 = x \times x \times x \times x}\)
ParthKohli
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'Mathematical form' is still ambiguous.
Raja99
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some stats people know may know
UnkleRhaukus
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\[\langle x^2\rangle =\sum\limits_{j=0}^\infty x^2 P(j)\]
ParthKohli
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lol
lgbasallote
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\[\int 2xdx\]
Aryang
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this reminds me of a very fundamental/basic question in calculus..please see my next question..i'll post link..
lgbasallote
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\[\frac{d}{dx} (\frac{x^3}{3})\]
UnkleRhaukus
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what are you doing at @lgbasallote ,
lgbasallote
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\[x^2 = r^2 - y^2\]
lgbasallote
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trying to get all that's x^2 and see if anythign suits him
UnkleRhaukus
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im pretty sure i have provided the answer to the question
lgbasallote
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we all think that...
UnkleRhaukus
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,oh
Raja99
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i need E(x^2)=?
UnkleRhaukus
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the expectiation value of \(x\) \[\langle x\rangle =E(x)\]
Raja99
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@UnkleRhaukus yes but x^2
lalaly
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\[Var(x)=E(x^2)-(E(x))^2\]
Raja99
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i got the ans... thanks all
UnkleRhaukus
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\[\sigma_x=\langle x^2\rangle-\langle x\rangle ^2\]
lalaly
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:D
Raja99
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ya ur right
UnkleRhaukus
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The expectation value , or expect value of a function
is \[\langle f(x)\rangle =\sum\limits_{x=0}^\infty f(x)P(x)\]
where \(P(x)\) is the probability of x
Raja99
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yes for a discrete random variable
UnkleRhaukus
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im not sure why i put j instead of x,
UnkleRhaukus
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oh, you want a continuous function?
Raja99
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no i know
Raja99
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thank you
UnkleRhaukus
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\[\langle f(x)\rangle=\int\limits_{-\infty}^\infty f(x)\rho(x)\text dx\]
Raja99
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ya
UnkleRhaukus
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where \(\rho(x)\) is the probability density
UnkleRhaukus
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so
\[\langle x^2\rangle=\int\limits_{-\infty}^\infty x^2\rho(x)\text dx\]
Raja99
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@UnkleRhaukus small question the E(constant) is a constant right
UnkleRhaukus
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if the distribution of the variable \(x\) is constant , yes
Raja99
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thanks