Let the salt and pepper noise have the following pdf:

Obtain the mean and variance of this distribution.

The given probability density function (pdf) describes salt and pepper noise, a type of image noise characterized by randomly occurring white and black pixels in an image. The pdf is defined as follows:

\[ F(Z) = \begin{cases} 
P_{b} & \text{if } z ______ ______ ________ _______ _____ ___ _____ ____ _____ ___.
___ ______ ____ ________ _____ ____ __________ _______ _____ ____ __________ ___.
___ ______ ______ ____ ____ ______.
____ ________ ______ _____ ___ __________ _____ _________ ____.
____ ______ ___ ______ _________ ______ ____ ________ ____ _________.
___ ________ ______ _______ _________ _____ ____ ______ ___ ____.
_____ ________ ___ _____ ___.
_______ ___ _______ _______ ____ ________ __________.
____ _____ ___ ____ _____ ____ ____ ______ ____.
___ _______ ___ _________ ___ ____ _________ __________ ____ ___ ___ ___.
_____ _________ _________ ___ _____ ______ ______ _____ __________ _________.
___ ________ _____ _________ ____.
________ __________ ____ _______ _______ ____ _____ _________ ____ _________ ___.
________ ______ _____ _________ _________ __________ ______ ___.
________ ___ _________ _________ __________ ___ _________ ________ ___ ______ __________ ___.
_________ ______ __________ ____ ________ __________ _______ __________ ________.
_______ _______ ________ _______ __________ ________ ___.
________ ______ ______ ________ _________ _____ ____.
_________ _______ _________ ________ ____ __________ _______ ___ _____.
___ ______ ___ _______ ____ ____ ______.
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