Note on Probability Density Functions * Intuition. Given 6>0, Pr(X e is equal to the integral of f(x) over Therefore, if € is "small" f(x) Pr(X e Even if f(x) is not a probability, it can be used to obtain relative probability of one value Xl over in that Pr(X € [Xl-€, Xl +e])/Pr(X € [X2-e, +6]) 26 Thus, if f(X1) is larger than f(X2), then values of X close to Xl are more likely than values close to ( * ) Advanced material
Question
Note on Probability Density Functions * Intuition. Given 6>0, Pr(X e is equal to the integral of f(x) over Therefore, if € is "small" f(x) Pr(X e Even if f(x) is not a probability, it can be used to obtain relative probability of one value Xl over in that Pr(X € [Xl-€, Xl +e])/Pr(X € [X2-e, +6]) 26 Thus, if f(X1) is larger than f(X2), then values of X close to Xl are more likely than values close to ( * ) Advanced material
Solution
Nota sobre Funciones de Densidad de Probabilidad *
Intuición. Dado 6>0, Pr(X ∈ [x]) es igual a la integral de f(x) sobre [x]. Por lo tanto, si € es "pequeño", f(x) Pr(X ∈ [x]) se puede aproximar.
Incluso si f(x) no es una probabilidad, se puede utilizar para obtener la probabilidad relativa de un valor X1 sobre otro X2, de tal manera que Pr(X ∈ [X1-€, X1 +€])/Pr(X ∈ [X2-€, X2 +€]).
Así, si f(X1) es mayor que f(X2), entonces los valores de X cercanos a X1 son más probables que los valores cercanos a X2.
(*) Material avanzado.
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