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Quantizer. Let X ~ Exp(A), i.e., an exponential random variable with parameter A and Y = [X], i.e., Y = k for k < X < k + 1, k = 0,1, 2,.... (a) Find the pmf of Y. (b) Find the pdf of the quantization error Z = X – Y.

Quantizer. Let X ~ Exp(A), i.e., an exponential random variable with parameter A and Y = [X], i.e., Y = k for k < X < k + 1, k = 0,1, 2,.... (a) Find the pmf of Y. (b) Find the pdf of the quantization error Z = X – Y.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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pdf means probability density fun c tuo n

**Quantizer** Let \( X \sim \text{Exp}(\lambda) \), i.e., an exponential random variable with parameter \(\lambda\) and \(Y = \lfloor X \rfloor\), i.e., \(Y = k\) for \(k \leq X < k + 1\), \(k = 0, 1, 2, \ldots\). (a) Find the pmf of \(Y\). (b) Find the pdf of the quantization error \(Z = X - Y\).
Transcribed Image Text:**Quantizer** Let \( X \sim \text{Exp}(\lambda) \), i.e., an exponential random variable with parameter \(\lambda\) and \(Y = \lfloor X \rfloor\), i.e., \(Y = k\) for \(k \leq X < k + 1\), \(k = 0, 1, 2, \ldots\). (a) Find the pmf of \(Y\). (b) Find the pdf of the quantization error \(Z = X - Y\).
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