Thread: prob and stat inference-sets review
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Old August 21st, 2008, 12:44 AM
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Quote:
Originally Posted by kid funky fried View Post
I need to review sets for my probability and statistical inference course.
I do not understand the meaning of the following:

\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 A_{k} for k = 1, 2, 3, .....

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

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

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

etc.

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


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