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The Law of Large Number, draw i.i.d examples of a random variable y, then with propability of 1 the average of y_1, ... y_n goes to the expected value of y.

When i apply a function to the y_i's, does then also hold that the average of f(y_1), ... f(y_n) goes to the expected value of f(y).

Does the function f needs to fullfil certain conditions for this to hold?

user3680510
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  • Would writing "$f(y_i)$" as "$x_i$" help? – whuber Feb 13 '19 at 12:48
  • @whuber It seems that $f(y_i)$ is just a sample of the random variablen $f(y)$. So it should still work however the mean and variance of the random variable changes, is this correct? – user3680510 Feb 13 '19 at 13:05
  • I find that very confusing: if the mean and variance of a "random variable" can change, then it's not a random variable anymore. Are you trying to model a stochastic process? In my comment I was trying to suggest that you simplify your notation and then forget how the $x_i$ were computed and focus on the fact that you have them. Is there any aspect of your situation that would prevent application of laws of large numbers to them? – whuber Feb 13 '19 at 13:23
  • @whuber no all i wanted to say is that the mean of y is different to f(y). No i don't think so – user3680510 Feb 13 '19 at 14:06

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