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.
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.
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 \(Z = X - Y\).
Definition Definition Probability of occurrence of a continuous random variable within a specified range. When the value of a random variable, Y, is evaluated at a point Y=y, then the probability distribution function gives the probability that Y will take a value less than or equal to y. The probability distribution function formula for random Variable Y following the normal distribution is: F(y) = P (Y ≤ y) The value of probability distribution function for random variable lies between 0 and 1.
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