For a random variable X, find E[Y] where Y=(X-E[X])/(standard deviation of X).

I've only tinkered with this a few minutes, and am working on it now but am not seeing it as terribly obvious. I'm just looking for a "Dude, its pretty straightforward, just keep tinkering" or a "Well, it ain't bad but without *this* or *that* identity, you're going to go cross-eyed staring at your page."

I just don't want to spend an hour on what may be a 3-minute algebra march.

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I found that expression used several times in a few different spots in my text. It seems like an important proportion, but there is no discussion nor even explicit mention of it solo. Maybe if someone could just explain what that proportion is briefly, the lights might come on for me...

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It zero, isn't it? If I think about Z=X-E[X], the mean (expectation) of Z is zero (this much is quite straightforward). The only difference between my Z and the Y in the problem statement is that Y is scaled by the standard deviation. I think E[Y]=0. Still, feel free to confirm this or shoot it down like a lame duck.