A researcher has computed the empirical distribution $F_n$ for a data set $x_1, x_2, . . . , x_n$. She discovers an extra data point, $x_{n+1}$. She wonders how $F_n$ is related to $F_{n+1}$, the empirical distribution function for the new data set. Which of the following statements is correct?

a) $F_{n+1}(x)=F_n(x)− \frac{1}{n+1}\:for\:−∞<x<∞$
b) $F_{n+1}(x)=F_n(x)+ \frac{1}{n+1}\:for\:−∞<x<∞$
c) $F_{n+1}(x_n) ≤ F_n(x_n)\:if\:x_n > x_{n+1}$
d) $F_{n+1}(x_2) ≤ F_n(x_2)\:if\:x_2 < x_{n+1}$
e) $F_{n+1}(x) = F_n(x)\:if\:x > x_{n+1}$
f) $F_{n+1}(x) = F_n(x)\:if\:x < x_{n+1}$

I have no clue how to find the correct answer (D) can someone help me?


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