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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
 one year 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)
 one year ago
 one year ago

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schmidtdancerBest ResponseYou've already chosen the best response.0
@ParthKohli @hba ??
 one year ago

schmidtdancerBest ResponseYou've already chosen the best response.0
(a) I know a is 0.4
 one year ago

mathmateBest ResponseYou've already chosen the best response.1
dw:1358086275602:dw Here's how you get it.
 one year ago

schmidtdancerBest ResponseYou've already chosen the best response.0
ok so a would then be 0.4?
 one year ago

mathmateBest ResponseYou've already chosen the best response.1
Yes, as you said. Remember the area under a probability distribution always add up to 1.0.
 one year ago

schmidtdancerBest ResponseYou've already chosen the best response.0
Ok! how do i find b?
 one year ago

mathmateBest ResponseYou've already chosen the best response.1
Probability(a<X<b)=area between the vertical lines a and b.
 one year ago

schmidtdancerBest ResponseYou've already chosen the best response.0
Ok! would d be .4 too then
 one year ago

mathmateBest ResponseYou've already chosen the best response.1
Can you repeat for d? Draw the diagram and check.
 one year ago

schmidtdancerBest ResponseYou've already chosen the best response.0
x is less then or eqaual to .6.....
 one year ago

schmidtdancerBest ResponseYou've already chosen the best response.0
im not sure how to find this probability?
 one year ago

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

mathmateBest ResponseYou've already chosen the best response.1
X varies from 0 to 1, so X<0.6 means from 0 to 0.6
 one year ago

mathmateBest ResponseYou've already chosen the best response.1
dw:1358086899713:dw
 one year ago

schmidtdancerBest ResponseYou've already chosen the best response.0
thats 60 % of the diagram
 one year ago

schmidtdancerBest ResponseYou've already chosen the best response.0
ok so d is .6? :)
 one year ago

mathmateBest ResponseYou've already chosen the best response.1
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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