What function is a probability density function on the interval ?

Question

What function is a probability density function on the interval  ?

Quizplus · Accepted Answer

Probability density functions (pdf) are non-negative for all values in their domain and integrate to 1 over the entire domain. The interval given in the question is a hexadecimal representation of numbers. Therefore, we cannot infer any properties of a pdf from this representation. So, we need to look at the options. 
Option A has an odd digit (a) in the third group, which means it is not a valid hexadecimal representation. The same problem applies to option B, which has an odd digit (a) in the fourth group. Option D has an odd digit (a) in the fifth group. Option E has an odd digit (7) in the fourth group. 
Only option C has valid hexadecimal digits in all groups, and therefore it could represent a valid pdf on the given interval.

What Function Is a Probability Density Function on the Interval