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What is this notation called and what does it mean? It's in regards to standardising a normal distribution

4 Answers

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In a literal sense, it's just saying that if a sample Y is just the adjusted version of another sample X, then you can find the mean of Y by adjusting the mean of X in the same way. It's also saying that you can find the standard deviation of Y in basically the same way (except that the shifting by *a* doesn't come into play)
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What are you trying to do with it? What is the distribution you are trying to standardise, and what random variable are you looking to find the probability for?

Say you had a normal distribution with a mean of 62, and a standard deviation of 30, and you wanted to know the probability of a random variable being 95 or less you would do this:

(95-62)/30 = 1.1.

Then you would look up 1.1 in the standard normal distribution table, which gives 0.84134 - which is the probability.
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Mean and variance (the s squareds)
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This is about linear regression.

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