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ti8623er

Statistics Question: Normal Distibution If Z is a standard normal random variable, what is: P(z^(2)<1) ??

  • one year ago
  • one year ago

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  1. amistre64
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    wouldnt that be a cumulative of z<1 ?

    • one year ago
  2. amistre64
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    |dw:1362004635659:dw| or am i misreading this?

    • one year ago
  3. amistre64
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    im prolly misreading it :/

    • one year ago
  4. ti8623er
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    the book (well the answers in the back) rewrite it as P(-1<Z<1), but i dont know why??? :/

    • one year ago
  5. amistre64
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    ahh, so i had the right idea sort of

    • one year ago
  6. ti8623er
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    i needs explanation please :)

    • one year ago
  7. amistre64
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    the reason why is because when you square a number it goes postive; and all the values of z that can be squared and be less than 1 are those values that are less than 1 to begin with.

    • one year ago
  8. amistre64
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    (-.5)^2 = .25 (-.9999)^2 = well something between 0 and 1 :)

    • one year ago
  9. ti8623er
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    i think it might be me but i sill dont understand

    • one year ago
  10. amistre64
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    |dw:1362005251278:dw|

    • one year ago
  11. amistre64
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    is 2^2 less than 1?

    • one year ago
  12. ti8623er
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    can we reason on it by appllying some properties of inequalitys o Z^2<1 ??

    • one year ago
  13. amistre64
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    sure

    • one year ago
  14. ti8623er
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    okay....

    • one year ago
  15. amistre64
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    z^2 < 1 sqrt each side z < sqrt(1) or z > -sqrt(1)

    • one year ago
  16. ti8623er
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    would it be or or and?

    • one year ago
  17. slaaibak
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    P(z^(2)<1) = P(-1< Z < 1) = \[\Phi (1) - \Phi(-1)\]

    • one year ago
  18. amistre64
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    .... picky picky picky, fine, the intersection

    • one year ago
  19. slaaibak
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    Also, Z^2 is is a chi squared distribution with 1 degree of freedom. So you can find the F(1) using the cumulative distribution function of the chi squared distribution

    • one year ago
  20. amistre64
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    or, another idea: \[|z|=\sqrt{z^2}\] \[z^2<1\] \[\sqrt{z^2}<\sqrt{1}\] \[|z|<1\]

    • one year ago
  21. amistre64
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    \[|z|<1~implies~-1<z<1\]

    • one year ago
  22. ti8623er
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    gracias everybody

    • one year ago
  23. amistre64
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    good luck :)

    • one year ago
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