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ENMA 420-520 Lecture 4 Slides

# ENMA 420-520 Lecture 4 Slides - Statistical Concepts for...

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Click to edit Master subtitle style 10/17/09 Statistical Concepts for Engineering Management ENMA 420 / 520 Lecture #4 Continuous Random Variables 11

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10/17/09 Continuous Random Variables The CDF F(y0) for a random variable Y is equal to the probability: F(y0) = P (Y <= y0), -∞ < y0 < ∞ A continuous random variable Y is one that has the following properties: Y takes on an infinitely countable number of values in the interval (-∞,∞). The CDF is continuous 22
10/17/09 Density Functions The density function for a continuous random variable Y is the derivative of the CDF: Therefore, we have: 33

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10/17/09 Properties of Density Functions Always positive: Normalized (area under curve = 1): Interval: 44
10/17/09 Exercise 5.2 55

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10/17/09 Exercise 5.2 (Cont’d) 66
10/17/09 Expected Values for Continuous Random For a CRV Y with density function f(y), and g(y) any function of y, then: and: 77

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10/17/09 Expected Value Theorems For a continuous random variable Y with a probability distribution p(y): The expected value of a constant is the constant; e.g. E[c] = c The expected value of a constant times Y is the constant times the expected value of Y; e.g. E[cY] = cE[Y] For a series of functions gk(Y), the 88
10/17/09 Variance The variance of a continuous random variable Y with probability distribution p(y) and E[Y] = μ is: The standard deviation is the (positive) square root of the variance of Y: 99

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10/17/09 Exercise 5.8 1010
10/17/09 Exercise 5.8 (Cont’d) 1111

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10/17/09 Exercise 5.8 (Cont’d) 1212
10/17/09 Exercise 5.8 (Cont’d) 1313

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10/17/09 Exercise 5.8 (Cont’d) 1414
10/17/09 5 minute Break What are the major differences between discrete and continuous random variables?

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