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schmidtdancer

  • 2 years ago

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)

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  1. schmidtdancer
    • 2 years ago
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    @ParthKohli @hba ??

  2. schmidtdancer
    • 2 years ago
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    (a) I know a is 0.4

  3. mathmate
    • 2 years ago
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    |dw:1358086275602:dw| Here's how you get it.

  4. schmidtdancer
    • 2 years ago
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    ok so a would then be 0.4?

  5. mathmate
    • 2 years ago
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    Yes, as you said. Remember the area under a probability distribution always add up to 1.0.

  6. schmidtdancer
    • 2 years ago
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    Ok! how do i find b?

  7. mathmate
    • 2 years ago
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    Probability(a<X<b)=area between the vertical lines a and b.

  8. schmidtdancer
    • 2 years ago
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    is it .6?

  9. mathmate
    • 2 years ago
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    Exactly!

  10. schmidtdancer
    • 2 years ago
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    c?

  11. mathmate
    • 2 years ago
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    Use your knowledge!

  12. schmidtdancer
    • 2 years ago
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    um....4?

  13. schmidtdancer
    • 2 years ago
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    .4?

  14. mathmate
    • 2 years ago
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    Yep! Good again!

  15. schmidtdancer
    • 2 years ago
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    Ok! would d be .4 too then

  16. schmidtdancer
    • 2 years ago
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    P(X <= 0.6)

  17. mathmate
    • 2 years ago
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    Can you repeat for d? Draw the diagram and check.

  18. schmidtdancer
    • 2 years ago
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    x is less then or eqaual to .6.....

  19. mathmate
    • 2 years ago
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    The area is....

  20. schmidtdancer
    • 2 years ago
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    hmm

  21. schmidtdancer
    • 2 years ago
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    im not sure how to find this probability?

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

  23. schmidtdancer
    • 2 years ago
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    .7?

  24. mathmate
    • 2 years ago
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    X varies from 0 to 1, so X<0.6 means from 0 to 0.6

  25. mathmate
    • 2 years ago
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    |dw:1358086899713:dw|

  26. schmidtdancer
    • 2 years ago
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    .6?

  27. schmidtdancer
    • 2 years ago
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    thats 60 % of the diagram

  28. mathmate
    • 2 years ago
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    Right again!

  29. schmidtdancer
    • 2 years ago
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    ok so d is .6? :)

  30. schmidtdancer
    • 2 years ago
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    and e is .53?

  31. mathmate
    • 2 years ago
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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!

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