3 The article \"Determination of the MTF of Positive Photoresists Using teh Monte Carlo Method\" (Photographic Sci. and Engr., 1983: 254-260) proposes the exponential distribution with parameter = 0.93 as a model for the distribution of a photon's free path length (m) under certain circumstances. Use this model with parameter = 0.93. f(x) = ex , x 0, 0 elsewhere 1. Calculate the expected path length, variance and standard deviation of path length 2. Calculate the probability that the path length exceeds 3.0 m 3. Calculate the probability the path length is between 1.0 and 3.0 m 4. Find the CDF For up to 5 points extra credit (turn in regardless of whether or not this problem is collected for exam credit): What value is exceeded by only 10% of all path lengths (the top 10%)? Show all work for partial credit (either by hand or in R)