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Here U have been generated uniformly from [0,1]. X is in the range[.4,.6]. What should the algorithm for this problem and how to plot it?

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Walter Roberson
Walter Roberson 2020-3-8

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When U is in [0,1] and X is any single value in that range, then the probability that is
When U is in [0,1] and X is a range of values in that range, you should not really be asking for : you should be asking for and in the uniform random case, that would be max(X)-min(X)

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what would be the implementation looks like?
Walter Roberson
Walter Roberson 2020-3-8
That depends upon whether you need to simulate the probabilities, or to calculate the probabilities.
Walter Roberson
Walter Roberson 2020-3-8
In order to simulate, you are going to need to break down the probability range into a number of "bins", such as every 0.01 probability. Let the number of bins be called N. Create a vector of counts, C, which is B long.
Now generate a random number, U. Multiply it by B, and take the ceiling. If you are using any of the MATLAB supplied random number generators, the result will be at least 1. Now add 1 to every entry in C that is indexed from 1 to that number.
Repeat this random number generation a number of times.
Now for any given entry in C, at index K, then C(K) is the probability that U was at least (K-1)/B

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