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10 cards from this deck
Probability distribution function
∫abf(x) dx\int_{a}^{b} f(x)\,dx∫abf(x)dx
f(x)≥0f(x) \geq 0f(x)≥0 (non-negativity)
∫−∞+∞f(x) dx=1\int_{-\infty}^{+\infty} f(x)\,dx = 1∫−∞+∞f(x)dx=1
∫−∞Mf(x) dx=12\int_{-\infty}^{M} f(x)\,dx = \frac{1}{2}∫−∞Mf(x)dx=21
Where pdf reaches its maximum value
∫−∞+∞xf(x) dx\int_{-\infty}^{+\infty} xf(x)\,dx∫−∞+∞xf(x)dx
E(X2)−μ2E(X^2) - \mu^2E(X2)−μ2
aE(X)+baE(X) + baE(X)+b
a2Var(X)a^2\text{Var}(X)a2Var(X)
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