- #1
xeon123
- 90
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I was looking to a video about cumulative distribution function () and he show the following function:[itex] \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ | 1/4, 0 \leq x \leq1 \\
f(x) =<(x^3)/5, 1 \leq x \leq 2 \\
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |0, otherwise.[/itex]
At minute 8:45, he presents the cumulative distribution as:[itex]
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ | 0, x \leq 0 \\
F(x) = < \frac{1}{4}x, 0 \leq x \leq 1 \\
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ | \frac{1}{20}(x^4+4), 1 \leq x \leq 2 \\
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ | 1, \ x \geq 2
[/itex]
I don't understand why F(x) is 1 for [itex]x \geq 2 [/itex], if f(x) is 0, otherwise. Why?BTW, I hope that that my functions are legibles, because I don't know how to put big curly brackets.
f(x) =<(x^3)/5, 1 \leq x \leq 2 \\
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |0, otherwise.[/itex]
At minute 8:45, he presents the cumulative distribution as:[itex]
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ | 0, x \leq 0 \\
F(x) = < \frac{1}{4}x, 0 \leq x \leq 1 \\
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ | \frac{1}{20}(x^4+4), 1 \leq x \leq 2 \\
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ | 1, \ x \geq 2
[/itex]
I don't understand why F(x) is 1 for [itex]x \geq 2 [/itex], if f(x) is 0, otherwise. Why?BTW, I hope that that my functions are legibles, because I don't know how to put big curly brackets.
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