Question

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)

Answer 1

For the answer to the question above, you will find probabilities for continuous r.v.'s like P(a < X < b) you just find the area under the density curve (what you have called the distribution). In this case, that's finding the area of a rectangle which means that if you can calculate sq ft for carpeting, you can do this problem.

For example,
e) (0.76 - 0.23)*1 = 0.53

For this problem the answer is the area above the interval:
eg. the probability of a) is 0.4 x height or 0.4 x 1 = 0.4.
I hope I helped you with my answer