Continuous Random Variable (2). Families of Continuous Random Variables Uniform R.V. Exponential R.V. Gaussian R.V.

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Presentation transcript:

Continuous Random Variable (2)

Families of Continuous Random Variables Uniform R.V. Exponential R.V. Gaussian R.V.

Uniform Random Variable

Definition and Theorem

Application of Uniform Random Variable 3-bit quantizer 8-bit quantizer Source: Discrete-Time Signal Processing by Oppenheim

Quantizer Source: Discrete-Time Signal Processing by Oppenheim

Modeling the Quantization Error as a Uniform Random Variable Source: Discrete-Time Signal Processing by Oppenheim

Variance of Quantization Noise Source: Discrete-Time Signal Processing by Oppenheim

Exponential Random Variable

Examples of Exponential R.V.

Definition and Theorem

Gaussian Random Variable

Examples of Gaussian R.V. μ X =represents the location of the center of the bell σ X =represents the width of the bell

Definition and Theorem

Properties of Gaussian R.V. Proof:

Definition and Theorem

Application of Normal R.V.

Symmetry Properties of Gaussian PDF

Complementary CDF

Z=3, 3x of σ 3 σ is approximately 1/1000

Matlab

Sensitivity of an Inverting Amplifier Due to Resistor Mismatch

Gain of an Inverting Amplifier Probability Gain in dB

Project Optional Reference (Sedra Smith) Instrumentation Amplifier (Section 2.4.2) Mismatch due to gm (Section 8.2.5)

Optional Materials

Exponential & Geometric Random Variable

Examples of Exponential R.V.

Conditioning a Continuous R.V.