# Chapter3-1 - Continuous Random Variables Reading Chapter...

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1 Continuous Random Variables Reading: Chapter 3.1 – 3.8 Homework: 3.1.2, 3.2.1, 3.2.4, 3.3.2, 3.3.7 G. Qu ENEE 324 Engineering Probability 2 Cumulative Distribution Function CDF of a random variable X is: F X (x) = P[X≤x] X is a continuous random variable is F X (x) is continuous. (the range of X contains a continuous interval) Example: X: a random integer between 0 and 4. S X ={0,1,2,3,4} P X (x) = 0.2 for x=0,1,2,3,4 and 0 otherwise F X (x) is an non-decreasing piece-wise constant function that is not continuous at x=0,1,2,3,4 Y: a random real number between 0 and 4. S Y =[0,4] is a continuous region, not a countable set. F Y [y] = P[Y≤y] = ? P Y [Y=y] = ? > < = 4 1 4 0 4 / 0 0 ) ( y y y y y F Y

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2 G. Qu ENEE 324 Engineering Probability 3 Properties of CDF Theorem 3.1: for any random variable X F X (-∞) = 0, F X (∞) = 1 F X (x) = 0 for x<x min , F X (x) = 1 for x ≥x max F X (x) ≥ F X (x’) if x≥x’ F X (x) – F X (x’) = P[x’< X ≤ x] Example: Quiz 3.1
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Chapter3-1 - Continuous Random Variables Reading Chapter...

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