Raja99 3 years ago what is the expected value of x^2 in mathematical form?

1. Raja99

in a simplified form

2. lgbasallote

what do you mean?

3. ParthKohli

$$x \times x$$ I think that's what you mean.

4. Raja99

yeah

5. lgbasallote

mathematical form?

6. ParthKohli

Hmm. Similarly: $$\color{Black}{\Rightarrow x^3 = x \times x\times x}$$ $$\color{Black}{\Rightarrow x^4 = x \times x \times x \times x}$$

7. ParthKohli

'Mathematical form' is still ambiguous.

8. Raja99

some stats people know may know

9. UnkleRhaukus

$\langle x^2\rangle =\sum\limits_{j=0}^\infty x^2 P(j)$

10. ParthKohli

lol

11. lgbasallote

$\int 2xdx$

12. Aryang

this reminds me of a very fundamental/basic question in calculus..please see my next question..i'll post link..

13. lgbasallote

$\frac{d}{dx} (\frac{x^3}{3})$

14. UnkleRhaukus

what are you doing at @lgbasallote ,

15. lgbasallote

$x^2 = r^2 - y^2$

16. lgbasallote

trying to get all that's x^2 and see if anythign suits him

17. Aryang
18. UnkleRhaukus

im pretty sure i have provided the answer to the question

19. lgbasallote

we all think that...

20. UnkleRhaukus

,oh

21. Raja99

i need E(x^2)=?

22. UnkleRhaukus

the expectiation value of $$x$$ $\langle x\rangle =E(x)$

23. Raja99

@UnkleRhaukus yes but x^2

24. lalaly

$Var(x)=E(x^2)-(E(x))^2$

25. Raja99

i got the ans... thanks all

26. UnkleRhaukus

$\sigma_x=\langle x^2\rangle-\langle x\rangle ^2$

27. lalaly

:D

28. Raja99

ya ur right

29. UnkleRhaukus

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

30. Raja99

yes for a discrete random variable

31. UnkleRhaukus

im not sure why i put j instead of x,

32. UnkleRhaukus

oh, you want a continuous function?

33. Raja99

no i know

34. Raja99

thank you

35. UnkleRhaukus

$\langle f(x)\rangle=\int\limits_{-\infty}^\infty f(x)\rho(x)\text dx$

36. Raja99

ya

37. UnkleRhaukus

where $$\rho(x)$$ is the probability density

38. UnkleRhaukus

so $\langle x^2\rangle=\int\limits_{-\infty}^\infty x^2\rho(x)\text dx$

39. Raja99

@UnkleRhaukus small question the E(constant) is a constant right

40. UnkleRhaukus

if the distribution of the variable $$x$$ is constant , yes

41. Raja99

thanks