Thread: proving or disproving probabillity density function

Prove or disprove: If f1(x) and f2(x) are probability density functions and if θ1 + θ2 = 1, then θ1f1(x) + θ2f2(x) is a probability density function.


I do not know how to do this at all. Any help would be greatly appreciated.

Originally Posted by cielo

Prove or disprove: If f1(x) and f2(x) are probability density functions and if θ1 + θ2 = 1, then θ1f1(x) + θ2f2(x) is a probability density function.


I do not know how to do this at all. Any help would be greatly appreciated.

1. where the integrals are over the supports of each pdf.

But ....

2. Is where always true ....?

How nice! Thank you so much for the help!