Suppose that either of two instruments might be used for making a certain measurement. Instrument 1 yields a measurement whose p.d.f. is
f1(x)=2x, 0 <x<1
Instrument 2 yields a measurement whose p.d.f. is
f2(x)=3x^2, 0 <x<1
Suppose that one of the two instruments is chosen at random and a measurement X is made with it.
Determine the marginal p.d.f. of X.
If X = 1/4 what is the probability that instrument 1 was used?