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anonymous

  • one year ago

The probability distribution of X is given in the table. What is the variance of the distribution?

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  1. anonymous
    • one year ago
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    @rational

  2. anonymous
    • one year ago
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  3. rational
    • one year ago
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    start by finding the mean

  4. anonymous
    • one year ago
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    um .25?

  5. rational
    • one year ago
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    |dw:1432817965592:dw|

  6. rational
    • one year ago
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    do you mean `2.5` ?

  7. rational
    • one year ago
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    mean = 1*.4+2*.1+3*.1+4*.4 = 2.5

  8. anonymous
    • one year ago
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    yes 2.5 sorry.

  9. rational
    • one year ago
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    good, find the deviation from mean for each of the data values

  10. rational
    • one year ago
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    subtract mean from each data value

  11. anonymous
    • one year ago
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    sub. 2.5 to each point?

  12. rational
    • one year ago
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    Yes, work \(\large x_i - 2.5\) for each data value

  13. rational
    • one year ago
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    |dw:1432818405802:dw|

  14. anonymous
    • one year ago
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    -1.5, -.5, .5, 1.5

  15. rational
    • one year ago
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    square each of them

  16. rational
    • one year ago
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    \(\large (x_i-2.5)^2\)

  17. anonymous
    • one year ago
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    -2.25, -.25, .25, 2.25?

  18. rational
    • one year ago
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    |dw:1432818549729:dw|

  19. rational
    • one year ago
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    when you square, the negative sign disappears thats precicely the reason we square here ok

  20. rational
    • one year ago
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    (-1.5)^2 = +2.25 it is not -2.25

  21. anonymous
    • one year ago
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    ops, crap. I put it in my calculator wrong then. :/

  22. anonymous
    • one year ago
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    @rational so what do I do now?

  23. rational
    • one year ago
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    hey still here ?

  24. anonymous
    • one year ago
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    yeah.

  25. rational
    • one year ago
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    sry was on mobile

  26. rational
    • one year ago
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    okay where are we

  27. anonymous
    • one year ago
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    Its okay :) 2.25 fix from negative to positive :)

  28. rational
    • one year ago
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    |dw:1432819551531:dw|

  29. rational
    • one year ago
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    multiply each of those by the corresponding probabilities, then add them up

  30. rational
    • one year ago
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    |dw:1432819635519:dw|

  31. anonymous
    • one year ago
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    1.85

  32. rational
    • one year ago
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    Perfect! 1.85 is the variance

  33. rational
    • one year ago
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    we basically used below formula |dw:1432819854547:dw|

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