What is the significance of operating on random variables. Like finding E[x^2 + 3]

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I had read the wiki page about moments. But still unable to get the real life significance.

https://en.wikipedia.org/wiki/Moment_(mathematics)

It also says the second moment of the distribution is the variance. Does it mean E[x^2] is the variance ??

I also know variance is E[x^2]-(E[x])^2.

I am lost. Any input will help. Thanks.

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The second moment of $X$ about the mean is the variance. So if $\mu=E(X)$ is the mean, then the variance of $X$ is $$E((X-\mu)^2), \quad\text{or equivalently}\quad E((X-E(X))^2)\tag{1}.$$

The above is the usual definition of variance. However, a not very hard computation shows that the variance is always equal to $$E(X^2)-(E(X))^2.\tag{2}$$ The expression (2) for the variance is often more convenient for calculations than the more fundamental expression (1).