Solved Homework: Question: C) A third programmer wants to design a random number generator based on floating point numbers i…

c) A third programmer wants to design a random number generator based on floating point numbers in the interval 1 to 2. Would this give a fair distribution of pseudo-random numbers? Explain your answer.

c) A third programmer wants to design a random number generator based on floating point numbers in the interval 1 to 2. Would this give a “fair” distribution of “pseudo-random” numbers? Explain your answer.

Expert Answer


I believe a part of this is question was already answered. Request you to provide a bit of context for the problem rather than posting subparts independently.

A general answer would be no. As pointed out in the previous answer, the most efficient way to generate pseudo-random floating point number is to select a random integer of n bits. After casting it to a float and then divide it with 2n until the number comes in the range of [1,2). One will notice that irrespective of the value of n chosen, the distribution of the floats generated using this method are “approximately uniform”. That is, for any 0≤a<b<1, the probability of the output falling in the sub-interval [a,b) will differ from b−a by at most max(2-n,2-np). For n≤np, it will also be uniform such that each float value that can be generated by this method is generated with the same probability (2-n). On the other hand, it can also be said that floats will not be uniform because each float in the range (1,2] is equally likely to be generated because the density of representable floating point values is itself not uniform. Thus it is fundamentally not possible to generate pseudo-random floats that have a fair distribution in a range.

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