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schmidtdancer Group Title

Consider a uniform distribution created by a random number generator. The distribution looks like a square with a length of 1 and a height of 1. The random number generator creates any number between 0 and 1. Find the following probabilities: a) P(0 <= X <= 0.4) b) P(0.4 <= X <= 1) c) P(X > 0.6) d) P(X <= 0.6) e) P(0.23 <= X <= 0.76)

  • one year ago
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  1. schmidtdancer Group Title
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    @ParthKohli @hba ??

    • one year ago
  2. schmidtdancer Group Title
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    (a) I know a is 0.4

    • one year ago
  3. mathmate Group Title
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    |dw:1358086275602:dw| Here's how you get it.

    • one year ago
  4. schmidtdancer Group Title
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    ok so a would then be 0.4?

    • one year ago
  5. mathmate Group Title
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    Yes, as you said. Remember the area under a probability distribution always add up to 1.0.

    • one year ago
  6. schmidtdancer Group Title
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    Ok! how do i find b?

    • one year ago
  7. mathmate Group Title
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    Probability(a<X<b)=area between the vertical lines a and b.

    • one year ago
  8. schmidtdancer Group Title
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    is it .6?

    • one year ago
  9. mathmate Group Title
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    Exactly!

    • one year ago
  10. schmidtdancer Group Title
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    c?

    • one year ago
  11. mathmate Group Title
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    Use your knowledge!

    • one year ago
  12. schmidtdancer Group Title
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    um....4?

    • one year ago
  13. schmidtdancer Group Title
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    .4?

    • one year ago
  14. mathmate Group Title
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    Yep! Good again!

    • one year ago
  15. schmidtdancer Group Title
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    Ok! would d be .4 too then

    • one year ago
  16. schmidtdancer Group Title
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    P(X <= 0.6)

    • one year ago
  17. mathmate Group Title
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    Can you repeat for d? Draw the diagram and check.

    • one year ago
  18. schmidtdancer Group Title
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    x is less then or eqaual to .6.....

    • one year ago
  19. mathmate Group Title
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    The area is....

    • one year ago
  20. schmidtdancer Group Title
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    hmm

    • one year ago
  21. schmidtdancer Group Title
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    im not sure how to find this probability?

    • one year ago
  22. mathmate Group Title
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    The figure is similar to the one I drew, but the vertical line is at 0.6.

    • one year ago
  23. schmidtdancer Group Title
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    .7?

    • one year ago
  24. mathmate Group Title
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    X varies from 0 to 1, so X<0.6 means from 0 to 0.6

    • one year ago
  25. mathmate Group Title
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    |dw:1358086899713:dw|

    • one year ago
  26. schmidtdancer Group Title
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    .6?

    • one year ago
  27. schmidtdancer Group Title
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    thats 60 % of the diagram

    • one year ago
  28. mathmate Group Title
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    Right again!

    • one year ago
  29. schmidtdancer Group Title
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    ok so d is .6? :)

    • one year ago
  30. schmidtdancer Group Title
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    and e is .53?

    • one year ago
  31. mathmate Group Title
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    You do realize that we are dealing with a square of 1x1. So 0<X< 0.6 means simply 60% of the square. Sometimes, and most of the time, the distribution is not a straight line (uniform), the calculation may not be as easy. Such as this: |dw:1358087084888:dw| You're doing great with this particular case. ALSO NOTICE that we did not care between <= (less than or equal) and < less than. It is because P(x=0.6) is zero, because it is almost impossible for X to be exactly 0.6. Finally, for (e), you got it right again, congratulations!

    • one year ago
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