EECE7204 Problem Set 3
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EECE7204
Problem Set 3
Problem 1 (3.6). Let X be a Laplacian random variable with pdf
Let Y = g(X), where g(·) is the nonlinear function given as the saturable limiter
Find the distribution function FY (y).
Problem 2 (3.9). In homomorphic image processing, images are enhanced by applying nonlinear transformations to the image functions. Assume that the image function is modeled as RV X and the enhanced image Y is Y = ln X. Note that X cannot assume negative values. Compute the pdf of Y if X has an exponential density
Problem 3 (3.10). Assume that X ∼ N (0, 1) and let Y be defined by
Compute the pdf of Y .
Problem 4 (3.18). Let X and Y be independent and identically distributed exponential RVs with
Compute the pdf of Z = X − Y .
Problem 5 (3.22). The objective is to generate numbers from the pdf shown in Figure P5 (3.22). All that is available is a random number generator that generates numbers uniformly distributed in (0, 1). Explain what procedure you would use to meet the objective.
Problem 6 (3.27). Let Z = max(X1, X2), where X1 and X2 are independent and exponentially distributed random variables with pdf
(a) Find the distribution function of Z.
(b) Find the pdf of Z.
2023-12-01