Question

A parabolic satellite dish reflects signals to the dish’s focal point. An antenna designer analyzed signals transmitted to a satellite dish and obtained the probability density function

f(x)=cæ1- 1 x2öfor 0<x<2,whereXisthedistance(inmeters)fromthecentroidofthe ç 16 ÷

èø

dish surface to a reflection point at which a signal arrives. Determine the following:

1. Value of c that makes f (x) a valid probability density function

2. ?(? < 0.4

3. ?(0.1<?<0.4

4. ?(?)

5. ?(?)

Answer 1