Posted by
**Lucy** on
.

Particles are a major component of air pollution in many areas. It is of interest to study the sizes of contaminating particles. Let X represent the diameter, in micrometers, of a randomly chosen particle. Assume that in a certain area, the probability density function of X is inversely proportional to the volume of the particle; that is, assume that

where c is a constant.

c/x^4 x > or equal to 1

0 > 1

(a) Find the value of c so that is a valid probability density function.

(b) Find the mean particle diameter.

(c) Find the median particle diameter.

(d) The term refers to particles 10 or less in diameter. What proportion of the contaminating particles are ?

(e) The term refers to particles 2.5 or less in diameter. What proportion of the contaminating particles are ?

(f) What proportion of the particles are ?