The article “Determination of the MTF of Positive Photoresists Using the Monte Carlo Method” (Photographic Sci. Engr. 1983: 254–260) proposes the exponential distribution with parameter λ = .93 as a model for the distribution of a photon’s free path length (lm) under certain circumstances. Suppose this is the correct model.
a. What is the expected path length, and what is the standard deviation of path length?
b. What is the probability that path length exceeds 3.0? What is the probability that path length is between 1.0 and 3.0?
c. What value is exceeded by only 10% of all path lengths?