Problem 1:
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 λ = 0.93 as a model for the distribution of a photon's free path length (µm) under certain circumstances. Use this model with parameter λ = 0.93.
f(x) = λe-λx, 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 µm
3. Calculate the probability the path length is between 1.0 and 3.0 µm
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)