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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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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(a) I know a is 0.4
|dw:1358086275602:dw| Here's how you get it.

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ok so a would then be 0.4?
Yes, as you said. Remember the area under a probability distribution always add up to 1.0.
Ok! how do i find b?
Probability(a
is it .6?
Exactly!
c?
Use your knowledge!
um....4?
.4?
Yep! Good again!
Ok! would d be .4 too then
P(X <= 0.6)
Can you repeat for d? Draw the diagram and check.
x is less then or eqaual to .6.....
The area is....
hmm
im not sure how to find this probability?
The figure is similar to the one I drew, but the vertical line is at 0.6.
.7?
X varies from 0 to 1, so X<0.6 means from 0 to 0.6
|dw:1358086899713:dw|
.6?
thats 60 % of the diagram
Right again!
ok so d is .6? :)
and e is .53?
You do realize that we are dealing with a square of 1x1. So 0

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