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10 cards from this deck
Discrete: ∑\sum∑; Continuous: ∫\int∫
E(X)=∫abxf(x) dxE(X) = \int_a^b xf(x) \, dxE(X)=∫abxf(x)dx
The balancing point/average value
How spread out the distribution is
∫ab(x−μ)2f(x) dx\int_a^b (x - \mu)^2 f(x)\,dx∫ab(x−μ)2f(x)dx
∫abx2f(x) dx−μ2\int_a^b x^2 f(x)\,dx - \mu^2∫abx2f(x)dx−μ2
Method 2 - simpler algebra
σ=Var(X)\sigma = \sqrt{\text{Var}(X)}σ=Var(X)
SD: same as variable; Variance: squared units
Both give exactly the same answer
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