Normal distribution. f. X. Normal distribution. Are equally distributed random variables common in reality?. How does the distribution of a variable observable in nature typically look like?. f(x ). Normal distribution N(μ, σ 2 ) . μ. x. μ , σ . x = μ . Normal distribution.
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Are equally distributed random variables common in reality?
How does the distribution of a variable observable in nature typically look like?
Normal distribution N(μ, σ2)
μ , σ
x = μ Normal distribution
x f(x) 0
x - f(x) 0
f(x) maximal for
f(x) symmetric around μ
In R: dnorm() Densityfunction
X N(μ=140, σ2=100)
X N(μ=140, σ2=25)
X N(μ=160, σ2=100)
X N(μ=160, σ2=225)
Alteration of μ translation on the x-axis
Alteration σ dilationofthecurve
X N(μ, σ2)
Extension belowthecurveisthe total probability (=1).
P (X ≤ 150) =
N(0, 1)Normal distribution
LetX1,X2,…,Xnbeindependentandidenticallydistributedrandom variables withE(Xi)=μandVar(Xi)=σ² für i=1,..,n. Then, thedistributionfunctionsoftherandom variables sn=converge against thedistributionfunctionΦofthestandard normal distribution0,1).