Transcription of 18.440: Lecture 18 Uniform random variables
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18.440: Lecture 18 Uniform random variables
: Lecture 18 Uniform random variables Scott Sheffield MIT Lecture 18 1 Outline Uniform random variable on [0, 1] Uniform random variable on [ , ] Motivation and examples Lecture 18 2 Outline Uniform random variable on [0, 1] Uniform random variable on [ , ] Motivation and examples Lecture 18 3 Recall continuous random variable definitions Say X is a continuous random variable if there exists a probability density function f = fX on R such that P{X B} =f (x)dx :=1B (x)f (x) We may assumeR f (x)dx =f (x)dx = 1 and f is non-negative. b probability of interval [a, b] is given byf (x)dx, the area a under f between a and b.
Recall continuous random variable definitions Say X is a continuous random variable if there exists a probability density function . f = f. X. on R such that P{X ∈ B} = B. f (x)dx := 1. B (x)f (x)dx. ∞ We may assume. R. f (x)dx = −∞. f (x)dx = 1 and f is non-negative. b Probability of interval [a, b] is given by f (x)dx, the area. a ...
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