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# Pg 26 - 12 Discrete Random Variables o A discrete random...

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Unformatted text preview: 12 Discrete Random Variables o A discrete random variable is an outcome that takes 011 a ﬁnite number of values or emultably inﬁnite (such as an inﬁnite sequence of integers). Countable infinite means that for any twe ﬁnite values, there are a finite number (if values in between. . Let X be a discrete madam variable with probebiiity mass funetiun (pmf) pX(;r.) or P(X : I) The pmf describes the probability of each value of X. For p to be a proper probability distribution — P(X:;1:)>{Jfor all:r;EX , Z P(X - 1-) e 1 (11111 11, 1111 1(5) = 1. JEX 4mm - The CDF is prescribed as before and has the same properties 111111 : P1212111 : Z P1X=y1 ySIlyEX a Example: Consider a sequence of independent communication attempts, Where each attempt has a 70% chance of getting being received. Let X denute the number of communication attempts needed to get the ﬁrst successful communication. (a) What is the probability that the ﬁrst attempt is successful? 1 1 . Ix ,1 i n‘ 1'- .v‘ A .- Pi Flb ii} 1:11 I 513:" ﬁTi 3.111: m??? (ii‘Uiii’l \rij/ (b) “That Is the probability that that two attempts ate needed? _. .. 11,: ._ 1 . N 3} XDiEiQ-E):LE‘L 1?: C; “2: 111 11 ’1)? V1 . 7 1 if"?! ,1 1-,. .1 «a 1, 2 _ “- ‘. .2 - - f“. -11 ,1- 1 1 - I» 2 1 - Z 173') 1 -~ :2 1‘ 1,1 a... a: :‘u -1 ; 1-”: .- : 1 ‘r- ..._ 12 P611”? ‘~ '1 (i i 1’ 1, ‘1-1'1"<"1='v?(1 1" '~ . " ', i 1:; \ » ,1 , 1»\-~ .‘y 1 . : : , i ‘5: V 'F L 5&1"? 1"" i h/ A /.f" i ‘ ii 1'“ 3" ‘1‘ ‘* {1.3% 1-9314 1]: .1 M 1 '2 ...
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