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.
a. Find the value of c so that f (x) is a probability density function.
b. Find the mean particle diameter.
c. Find the cumulative distribution function of the particle diameter.
d. Find the median particle diameter.
e. The term 
refers to particles 10 µ mor less in diameter. What proportion of the contaminating particles are ?
f. The term 
refers to particles 2.5 µ mor less in diameter. What proportion of the contaminating particles are ?
g. What proportion of the particles are ?
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