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Continuous Random Variable (2)

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. Source: Discrete-Time Signal Processing by O ppenheim. 3-bit quantizer.

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Continuous Random Variable (2)

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  1. Continuous Random Variable (2)

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

  3. Uniform Random Variable

  4. Definition and Theorem

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

  6. Quantizer Source: Discrete-Time Signal Processing by Oppenheim

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

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

  9. Exponential Random Variable

  10. Examples of Exponential R.V.

  11. Examples of Exponential R.V.

  12. Definition and Theorem

  13. Gaussian Random Variable

  14. Examples of Gaussian R.V. μX=represents the location of the center of the bell σX=represents the width of the bell

  15. Definition and Theorem

  16. Properties of Gaussian R.V. Proof:

  17. Definition and Theorem

  18. Application of Normal R.V.

  19. Symmetry Properties of Gaussian PDF

  20. Complementary CDF

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

  22. Matlab

  23. Sensitivity of an Inverting Amplifier Due to Resistor Mismatch

  24. Gain of an Inverting Amplifier Probability Gain in dB

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

  26. Optional Materials

  27. Exponential & Geometric Random Variable

  28. Examples of Exponential R.V.

  29. Conditioning a Continuous R.V.

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