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anonymous
 4 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)
anonymous
 4 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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mathmate
 4 years ago
Best ResponseYou've already chosen the best response.1dw:1358086275602:dw Here's how you get it.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0ok so a would then be 0.4?

mathmate
 4 years ago
Best ResponseYou've already chosen the best response.1Yes, as you said. Remember the area under a probability distribution always add up to 1.0.

mathmate
 4 years ago
Best ResponseYou've already chosen the best response.1Probability(a<X<b)=area between the vertical lines a and b.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Ok! would d be .4 too then

mathmate
 4 years ago
Best ResponseYou've already chosen the best response.1Can you repeat for d? Draw the diagram and check.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0x is less then or eqaual to .6.....

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0im not sure how to find this probability?

mathmate
 4 years ago
Best ResponseYou've already chosen the best response.1The figure is similar to the one I drew, but the vertical line is at 0.6.

mathmate
 4 years ago
Best ResponseYou've already chosen the best response.1X varies from 0 to 1, so X<0.6 means from 0 to 0.6

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0thats 60 % of the diagram

mathmate
 4 years ago
Best ResponseYou've already chosen the best response.1You 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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