# Thread: prob and stat inference-sets review

1. ## prob and stat inference-sets review

I need to review sets for my probability and statistical inference course.
I do not understand the meaning of the following:

$\displaystyle \begin{gathered} A_k = \left\{ {x:\frac{{10}} {{k + 1}} \leqslant x \leqslant 10} \right\},k = 1,2,3,.... \hfill \\ \hfill \\ \bigcap\limits_{k = 1}^8 {A_k } = \left\{ {x:5 \leqslant x \leqslant 10} \right\} = A_1 \hfill \\ \end{gathered}$

2. Originally Posted by kid funky fried
I need to review sets for my probability and statistical inference course.
I do not understand the meaning of the following:

$\displaystyle \begin{gathered} A_k = \left\{ {x:\frac{{10}} {{k + 1}} \leqslant x \leqslant 10} \right\},k = 1,2,3,.... \hfill \\ \hfill \\ \bigcap\limits_{k = 1}^8 {A_k } = \left\{ {x:5 \leqslant x \leqslant 10} \right\} = A_1 \hfill \\ \end{gathered}$

The first statement defines the set $\displaystyle A_{k}$ for k = 1, 2, 3, .....

$\displaystyle A_1 = \{ x: \,5 \leq x \leq 10 \}$

$\displaystyle A_2 = \{ x: \,10/3 \leq x \leq 10 \}$

$\displaystyle A_3 = \{ x: \,5/2 \leq x \leq 10 \}$

etc.

$\displaystyle A_8 = \{ x: \,5/4 \leq x \leq 10 \}$

The second statement says that the intersection of the eight sets $\displaystyle A_1$, $\displaystyle A_2$, $\displaystyle A_3$, ....... $\displaystyle A_8$ is equal to $\displaystyle \{ x: \,5 \leq x \leq 10 \}$ (which is true by the way), which of course is just the set $\displaystyle A_1$.

3. ## Thanks! I think I...

I think I understand now.
The intersection is equal to A1 because A1 is the only set that would be common in all the other sets ( A2 through A8).

Thanks Again.

Kid