1. ## cumulative distribution function

Question attached.

2. It cannot be done unless you complete that table.
You have given no values for $f(x)$.

3. Sorry for confusion:

0 = 1/27
1 = 6/27
2 = 12/27
3 = 8/27

4. So for an answer maybe something along the lines...

F(x) = 0 if x<0
F(x) = 1/27 if 0<=x<1
F(x) = 6/27 if 1<=x<2
F(x) = 12/27 if 2<=x<3
F(x) = 8/27 if 3<=x

5. It will look like this:
$F_X (x) = \left\{ {\begin{array}{rc}
{0,} & {x < 0} \\
{\frac{1}
{{27}},} & {0 \leqslant x < 1} \\
?, & {1 \leqslant x < 2} \\
?, & ? \\
1, & {3 \leqslant x} \\\end{array} } \right.$

Now you fill in the blanks.

6. F(x) = 0 if x<0
F(x) = 1/27 if 0<=x<1
F(x) = 6/27 if 1<=x<2
F(x) = 12/27 if 2<=x<3
F(x) = 1 if 3<=x

Okay I see I did a mistake... it should be 1, not 8/27 for the 3<=x

7. No you missed the accumulation.
$
F_X (x) = \left\{ {\begin{array}{lc}
{0,} & {x < 0} \\
{\frac{1}
{{27}},} & {0 \leqslant x < 1} \\
{\frac{7}
{{27}}} & {1 \leqslant x < 2} \\
? & ? \\
1 & {3 \leqslant x} \\

\end{array} } \right.$

8. Ok I get it now. ACCUMULATION.... aka adding.

So we get 0+1/27+6/27+12/27=19/27.

Is my 2<=x<3 incorrect though?

9. Originally Posted by DINOCALC09
Is my 2<=x<3 incorrect though?
It is wrong also. Add the 'jump'.
When you finish $F_X(x)$ must be continuous on the right.

10. What do you mean by jump?

I know what continuous is kinda, but not sure how it relates to inequalities.

11. Originally Posted by DINOCALC09
What do you mean by jump?
It should go from $\frac{7}{27}$ to $\frac{19}{27}$.

That is a jump of $f(2)=\frac{12}{27}$.

12. yes, i see that. however, don't see what's wrong with the inequality necessarily. Should 2 not be inclusive?

13. Frankly this is tiresome. It is
$
F_X (x) = \left\{ {\begin{array}{lc}
{0,} & {x < 0} \\ \\
{\frac{1}
{{27}},} & {0 \leqslant x < 1} \\ \\
{\frac{7}{{27}}} & {1 \leqslant x < 2} \\ \\
{\frac{19}{{27}}} & {2 \leqslant x < 3} \\ \\
1 & {3 \leqslant x} \\

\end{array} } \right.$

I am done with the thread.