Calculus II

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For function `f` to be probability density function the following must hold


this is because probability of whole sample space must be 1. Hence we have



If we now return to our formula we get


`a=2` <--Your solution


In this case `P(0leqXleqt)` is actually expression for cumulative distribution function which we can calculate in following maner



But we have already calculated similar integral in the part a) so we know that it is equal to


Thus your solution is


In the image below blue is probability density function `f` and red is cumulative distribution function `P(0leqXleqt).`  

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