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CSE 221: Probabilistic Analysis of Computer Systems Topics covered: Continuous random variables Uniform and Normal distribution (Sec. 3.1, 3.4.6-3.4.7)

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Continuous random variables Discrete vs. Continuous random variables:

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Continuous random variables (contd..) Event definition: Cumulative Distribution Function (CDF):

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Continuous random variables (contd..) CDF of discrete vs. continuous random variables:

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Continuous random variable (contd..) Relationship between density and distribution functions:

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Continuous random variable (contd..) Properties of distribution function:

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Continuous random variables (contd..) Density function of continuous vs. discrete random variables:

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Uniform distribution (contd..) Density: Distribution function:

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Uniform distribution (contd..) Parameters of the uniform distribution: Verification of the CDF of uniform distribution:

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Normal distribution Density function: Shape of the density function:

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Normal distribution (contd..) Parameters of the normal distribution: Distribution function: Standard normal distribution:

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Normal distribution (contd..) Conversion of a non-standard random variable to a standard normal variable:

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Normal distribution (contd..) Example:

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Normal distribution (contd..) Central limit theorem:

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