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10 cards from this deck
Integration
E(X)=∫−∞∞xf(x) dxE(X) = \int_{-\infty}^{\infty} xf(x)\,dxE(X)=∫−∞∞xf(x)dx
Var(X)=E[X2]−μ2\text{Var}(X) = E[X^2] - \mu^2Var(X)=E[X2]−μ2
F(x)=P(X≤x)F(x) = P(X \leq x)F(x)=P(X≤x)
f(x)=ddxF(x)f(x) = \frac{d}{dx}F(x)f(x)=dxdF(x)
∫−∞∞f(x) dx=1\int_{-\infty}^{\infty} f(x)\,dx = 1∫−∞∞f(x)dx=1
F(M)=0.5F(M) = 0.5F(M)=0.5
E(R)=a+b2E(R) = \frac{a+b}{2}E(R)=2a+b
Var(R)=(b−a)212\text{Var}(R) = \frac{(b-a)^2}{12}Var(R)=12(b−a)2
f(r)=1b−af(r) = \frac{1}{b-a}f(r)=b−a1 for a<r<ba < r < ba<r<b
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