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Probability & Stochastic Processes. CH 2 Discrete Random Variables. CH 2.1 Definitions. Ex : S= { H, T }, random variable X. CH 2.1 Definitions. CH 2.1 Definitions. CH 2.2 Probability Mass Function (PMF). CH 2.2 Probability Mass Function (PMF).
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Probability &Stochastic Processes CH 2 Discrete Random Variables
CH 2.1 Definitions Ex : S={H, T}, random variable X
CH 2.2 Probability Mass Function (PMF) Ex 2.7 : Basketballtwo free draws, each shot good or bad equally likely S={gg, gb, bg, bb} Define random variable X be the point of the two shots.
CH 2.3 Families of Discrete Random Variables Ex 2.8 : Consider 3 experiments. 1) Tossing a coin: H or T → RV X = 0, 1 2) A phone number:Odd or Even → RV X = 0, 1 3) Modem bits: 0, 1 → RV X = 0, 1 … Very useful RV X with
CH 2.3 Families of Discrete Random Variables Ex 2.9,10,11 : IC test reject prob.p; RV X = 1 (success) accept prob.1-p; RV X = 0 (fail) Let RV Y: # of tests until first reject(success)
CH 2.3 Families of Discrete Random Variables • S or F test, S with prob. p, # of S in ntests
CH 2.3 Families of Discrete Random Variables • S or F test, S with prob. p, # of tests if we stop at the k-thS
CH 2.3 Families of Discrete Random Variables • QZ 2.3 : A modem transmits bits (0 or1). Prob. of error bit isp, 0<p<1. • Transmission continues until the firsterror; • Let RV X be the # of transmitted bits.
CH 2.5 Averages • 3 definitions of statistical average
HW #1(Do not submit ! But prepare the midterm exam.) • Textbook Problems: p44-46 • 1.5.2, 1.5.5., 1.6.3, 1.7.7 • Textbook Problems: p93-96 • 2.2.3, 2.2.6, 2.3.4, 2.3.6, 2.4.2, 2.5.4 Oh-Jin Kwon, EE dept., Sejong Univ., Seoul, Korea: http://dasan.sejong.ac.kr/~ojkwon/
CH 2.6 Functions of Random Variable Ex 2.27 : faxing, RV X : page #/ faxing r.v. Y : cost, 1-st page10 cent 2-nd page9 cent … 5-th page 6 cent 6~10-th page 50 cent reject more than 10 pages
CH 2.9 Conditional PMF ← Thrm 1.10 Law of Large Numbers
