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# notes_02 - MIT OpenCourseWare http/ocw.mit.edu 1.010...

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Unformatted text preview: MIT OpenCourseWare http://ocw.mit.edu 1.010 Uncertainty in Engineering Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu.terms . • • 1.010- Brief Notes # 2 Random Variables: Discrete Distributions Discrete Distributions • Probability Mass Function (PMF) P X ( x ) = P ( X = x ) = P ( O ) all O: X ( O )= x • Properties of PMFs 1. ≤ P X ( x ) ≤ 1 2. P X ( x ) = 1 all x Cumulative Distribution Function (CDF) F X ( x ) = P ( X ≤ x ) = P X ( u ) u ≤ x • Properties of CDFs 1. ≤ F X ( x ) ≤ 1 2. F X ( −∞ ) = 0 3. F X ( ∞ ) = 1 4. if x 1 > x 2 , then F X ( x 1 ) ≥ F X ( x 2 ) Discrete distributions (a) Probability Mass Function PMF (b) Cumulative Distribution Function CDF 1 2 • Examples of discrete probability distributions Bernoulli distribution • ⎧ ⎨ 1 , if an event of interest occurs (success) Y = ⎩ , if the event does not occur (failure) Y is called a Bernoulli or indicator variable ⎧ ⎨ p, y = 1 P...
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notes_02 - MIT OpenCourseWare http/ocw.mit.edu 1.010...

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