Posted by **Salman** on Thursday, December 2, 2010 at 1:16pm.

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.

(a)

Determine the marginal p.d.f. of X.

(b)

If X = 1/4 what is the probability that instrument 1 was used?