- #1
jwqwerty
- 43
- 0
Let X be random variable and X~N(u,σ^2)
Thus, normal distribution of x is
f(x) = (1/σ*sqrt(2π))(e^(-(x-u)^2)/(2σ^2)))
If we want to standardize x, we let z=(x-u)/σ
Then the normal distribution of z becomes
z(x) = (1/σ*sqrt(2π))(e^(-(x^2)/(2))
and we usually write Z~N(0,1)
But as you can see, sigma in z(x) does not disappear. Thus, in my opinion Z~N(0,1) should be actually written as Z~(1/σ)N(0,1). So here goes my question :
why does every textbook use the notation Z~N(0,1), not Z~(1/σ)N(0,1)
Thus, normal distribution of x is
f(x) = (1/σ*sqrt(2π))(e^(-(x-u)^2)/(2σ^2)))
If we want to standardize x, we let z=(x-u)/σ
Then the normal distribution of z becomes
z(x) = (1/σ*sqrt(2π))(e^(-(x^2)/(2))
and we usually write Z~N(0,1)
But as you can see, sigma in z(x) does not disappear. Thus, in my opinion Z~N(0,1) should be actually written as Z~(1/σ)N(0,1). So here goes my question :
why does every textbook use the notation Z~N(0,1), not Z~(1/σ)N(0,1)
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