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Thread: prob and stat inference-sets review

  1. #1
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    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}
    $






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  2. #2
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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:

    $\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 $\displaystyle A_1$.
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  3. #3
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    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
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