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)

The rigorous way to do this would be to compute a few integrals, but less work is usually better. Each of these probabilities correspond to the areas of rectangles. Each rectangle will have a height of 1, and the probability of interest will tell you everything you need to know about their lengths.





Alternatively, you can use the fact that to get the same result.