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10 cards from this deck
Variable that can take any value within a specific interval
Continuous: any value in range; Discrete: specific separated values
Pr(X=x)=0\Pr(X = x) = 0Pr(X=x)=0 for all xxx
Function representing probability distribution of continuous variable
f(x)≥0f(x) \geq 0f(x)≥0 for all xxx (always non-negative)
∫−∞∞f(x) dx=1\int_{-\infty}^{\infty} f(x) \, dx = 1∫−∞∞f(x)dx=1 (total area equals 1)
As areas under the PDF curve
Pr(a<X<b)=∫abf(x) dx\Pr(a < X < b) = \int_a^b f(x) \, dxPr(a<X<b)=∫abf(x)dx
Yes, f(x)f(x)f(x) values are not probabilities themselves
Pr(a<X<b)=Pr(a≤X≤b)\Pr(a < X < b) = \Pr(a \leq X \leq b)Pr(a<X<b)=Pr(a≤X≤b) (endpoints don't matter)
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