Chapter 3

# Chapter 3 - Chapter 3. Random Variables and Probability...

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Chapter 3. Random Variables and Probability Distributions 3.1 Random Variable random variable ( r.v. ) : is a function that associates a real number with each element in the sample space R x : the range of random variable X is the set of values which X can have sample space real numbers X

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Discrete r.v. : if R x is finite or countable infinite set ex) X = sum of two die, Y = no. of defect on a CD Continuous : if R x is uncountable infinite set ex) X = weight of a can coffee
3.2 Discrete Probability Distributions Probability function (pmf, probability distribution) () ( ) f xP X x = = : Properties 1) () 0 fx 2) () 1 x = 3) ( ) P Xx f x == Cumulative distribution function (cdf) ( ) ( ) ( ) ( ) tx Fx PX x ft x = ≤= < < : Properties 1) 0 F −∞ = 2) F ∞= 3) is a non-decreasing function 4) is continuous from the right

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Random experiment : Toss a fair coin 3 times X : no. of Heads in 3 times R x = {0, 1, 2, 3} 1 (0) 8 f = 3 (1) 8 f = 3 (2) 8 f = 1 (4) 8 f = (0 ) Px < = ?
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## This note was uploaded on 10/02/2011 for the course STAT 3011 taught by Professor Wang,zhan during the Spring '09 term at Minnesota.

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Chapter 3 - Chapter 3. Random Variables and Probability...

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