Lecture 03-RV and distribution

Lecture 03-RV and distribution - 1036: Probability &...

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Prob. & Stat. Lecture03 - random variables and probability distributions (cwliu@twins.ee.nctu.edu.tw) 3-1 1036: Probability & Statistics 1036: Probability & 1036: Probability & Statistics Statistics Lecture 3 Lecture 3 Random Variables Random Variables and Probability Distributions and Probability Distributions
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Prob. & Stat. Lecture03 - random variables and probability distributions (cwliu@twins.ee.nctu.edu.tw) 3-2 Random Variables • Experiments are conducted with results that are subject to chance • One is naturally concerned with the number of defectives that occur • A random variable, denoted by X , is a function that associates a real number, x X ,witheach element in the sample space S . S ={ bad, good, excellent } X : random variable Foe this case, x X , x =1:bad, x =2:good, x =3: excellent Example:
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Prob. & Stat. Lecture03 - random variables and probability distributions (cwliu@twins.ee.nctu.edu.tw) 3-3 Discrete vs. Continuous • If a sample space contains a finite number of possibilities with as many elements as there are whole numbers, it is called a discrete sample space • A random variable is called discrete if its set of possible outcomes is countable • Discrete random variable, in practical case, represent count data • If a sample space contains an infinite number of possibilities equal to the number of points on a line segment, it is called a continuous sample space • A random variable is called continuous if it can take on values on a continuous scale • Continuous random variable, in practical case, represent measured data
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Prob. & Stat. Lecture03 - random variables and probability distributions (cwliu@twins.ee.nctu.edu.tw) 3-4 Discrete Probability Distribution • The set of ordered pairs ( x , f ( x )) is a probability distribution of the discrete random variable X if, for x X , we have ). ( ) ( . 3 . 1 ) ( . 2 . 0 ) ( . 1 x f x X P x f x f x = = =
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Prob. & Stat. Lecture03 - random variables and probability distributions (cwliu@twins.ee.nctu.edu.tw) 3-5 Example • 8 computers with 3 defective ones. Find the probability distribution of having 0, 1, & 2 defective computers in selected 2 computers? Solution X : random variable for 3 defective computers x X is the values of possible numbers of defective computers been selected – There are 3 cases: x = 0 , zero defective computer in selected 2 computers x = 1 , 1 defective computer in selected 2 computers x = 2 , 2 defective computers in selected 2 computers
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Prob. & Stat. Lecture03 - random variables and probability distributions (cwliu@twins.ee.nctu.edu.tw) 3-6 Example, cont. 28 10 2 8 2 5 0 3 ) 0 ( ) 0 ( = = = = = X P x f 28 15 2 8 1 5 1 3 ) 1 ( ) 1 ( = = = = = X P x f 28 3 2 8 0 5 2 3 ) 2 ( ) 2 ( = = = = = X P x f (discrete) Probability distribution of X is x 0 12 f ( x ) 10/28 15/28 3/28 1 ) ( 2 0 = = x x f
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Prob. & Stat. Lecture03 - random variables and probability distributions (cwliu@twins.ee.nctu.edu.tw)
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Lecture 03-RV and distribution - 1036: Probability &...

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