# How $F_n$ is related to $F_{n+1}$

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) $$F_{n+1}(x)=F_n(x)− \frac{1}{n+1}\:for\:−∞
b) $$F_{n+1}(x)=F_n(x)+ \frac{1}{n+1}\:for\:−∞
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?