Lecture9_ContinuousRVs

Lecture9_ContinuousRVs - ECE 340 Probabilistic Methods in...

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1 ECE 340 Probabilistic Methods in Engineering M/W 3-4:15 Prof. Vince Calhoun Prof. Vince Calhoun Lecture 9: Continuous RVs Lecture 9: Continuous RVs
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2 Quiz • Write down the pmf for a Bernoulli random variable • What is the relationship between a Bernoulli and a Binomial random variable? • Write down the pmf for a Binomial random variable?
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3 Reading • This class: Section 4.1-4.3 • Next class: Section 4.4-4.5
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4 Outline • Section 4.1-4.3 • Continuous RV’s • CDF •PDF • Expected value of X
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5 Continuous Random Variables. As mentioned previously, not all r.v.s are discrete. Today we will study the continuous r.v. (the 2 nd general type of random variable) that arises in many applied problems
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6 Continuous Random Variables A discrete R.V. is one whose possible values either constitute a finite set or else can be listed in an infinite sequence (a list where there is a first element, a second, and so on) i. Def: A r.v. X is said to be continuous if its set of possible values is an entire interval of numbers ii. Rule of thumb: before the experiment is run, if you can determine/list all possible values of the random variable, it is a discrete random variable, else it is a continuous random variable.
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7 Continuous Random Variables i. Let X be a continuous r.v. The probability distribution or probability density function (p.d.f.) of X is a function f(x) [i.e. p(x)] such that for any 2 numbers a and b with a < b = b a dx x f b x a P ) ( ) ( that is, the probability X takes on a value in the
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This note was uploaded on 02/10/2010 for the course TBE 2300 taught by Professor Cudeback during the Spring '10 term at Webber.

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Lecture9_ContinuousRVs - ECE 340 Probabilistic Methods in...

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