Solution manual for probability statistics and random processes for electrical engineering 3 e 3rd e

Solution Manual for Probability, Statistics, and Random Processes For Electrical Engineering,

3/E 3rd Edition Alberto Leon-Garcia

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A Leon-Garcia INSTRUCTOR'S SOLUTIONS MANUAL Probability, Statistics, and Random Processesfor Electrical Engineering Chapter 3: Discrete Random Variables 3.1 The Notion of a Random Variable 3-1 c { 2. ~ Ce, ) (0 (2 t ,0 ) ,2 2 20) e9, '9 %, no«pp.A c 2 c 2.. ( 2 2 2 2 2

-d A. Leon-Garcia INSTRUCTOR'S SOLUTIONS MANUAL 3-2 Probability, Statistics, and Random Processesfor Electrical Engineering s 22 -14t€ 2pa]-44'k r x-Gd= r=it-gr? 'H:]=gt% 2,44# +dts isf 3+& --v"'"Y 4 G .9 t o 4 7 < -# oO f I "pr-sz«.Jr# r-a-ris,«·2i -< pg-le[t«4a"> i J

• 23 t5 3 , N 32 i A Leon-Garcia INSTRUCTOR'S SOLUTIONS MANUAL Probability, Statistics, and Random Processesfor Electrical Engineering 3-3 $'$' cuc coo t It Oc I O « t U U J U 1s 0 1. .24= 4, = 30 cc L'l a / / I I 4 %° t !l j n.• . ; i ; %4°

.J, N r 4° 4 tw3) z =.«4a+, . > ) ! i J ) 4 A Leon-Garcia INSTRUCTOR'S SOLUTIONS MANUAL Probability, Statistics, and Random Processesfor Electrical Engineering 3-4 Pu«A at {aw s[et ' 2 - t #2 A. ed A;B, 9AB co s»gut g$+ . < < e[A@;3,]= [ 2']+r.]= 4-rlz« ' A &) 7[x-«]= r[G-9fl«was, 4s«cl= dj] G. 0oo, {I I 0/0 tot, do f liO /t,D o I( 1 l 4 .£ N 4 4 2 3 3 P[=27=[{a««}]= ' rLx=]=e] e,'}] # rj=«1=·]}@•·]7#

ta 0 1 ± • A Leon-Garcia INSTRUCTOR'S SOLUTIONS MANUAL Probability, Statistics, and Random Processesfor Electrical Engineering 3-5 (3.7) 2.. 2640i5 ·lot 2A b4 ;J,..J. 4-a.. Aq 5 • 4, ¥ 4, X 2 l ' l 5 ' 2 4, X s] 5l < 9 21.%.46ls %dt- vwt-cs >, 1±4% - - 34 So -f & oo=. hul• 4£ -pob.ht .d !- o = t ' oo 51 P[=2)= 3I 1 ±¢ 4% Pf=9 %e 50 sl ;«Po pl x=to oo

A Leon-Garcia INSTRUCTOR'S SOLUTIONS MANUAL Probability, Statistics, and Random Processesfor Electrical Engineering

39)@ 44s.- 44 4al»

la. uwhv k ea -wu

~ s- = f-11t,-"Y\+2.) '" ,-n-J.)')i} - 'y t

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PI v=]=P[--=%]= r[•= z;;]

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s=Es,··k -=;o •

au-bod par o cv4 '

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s=E'.,,2"? kw tt ad<- 4&. -ltd t .a4do.h-.

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± } cs ° <°2o 4 ( I A Leon-Garcia INSTRUCTOR'S SOLUTIONS MANUAL Probability, Statistics, and Random Processesfor Electrical Engineering 3-7 3.2 Discrete Random Variables And Probability Mass Function P,,/. ) 8 7 R,( %, ~ lt t% @ % T o ± 2 k c) 2 %e l!- valve {( /te 3we, fda lats -lit l 94 Clao> cbloA• Ca •o ( 2 Pl.]= t - I c c> f 2 '4 n0rd.& I '% PL I Y-j= 1.4£.5+6.4 2 (% 2 '7¢ 2 ts 4 2 2 2 464 2 % 2o / 4% 4l - 4 I4 <( +[2] 43 p .() L g9 '%• 0 t 2

a p=± 1 7' t 2 % q 4 A Leon-Garcia INSTRUCTOR'S SOLUTIONS MANUAL Probability, Statistics, and Random Processesfor Electrical Engineering as 3-8 ±=nr #4±+5+, 2s & 2zs P5 2 , = -4 , t e=2 25 2 25 37 25 42%¢ l l l t ;, 1=7( 4+a+±)=S J , p7 1 s 2 s _ ? 4 21 a£ p -l I 1 1= g 7r &° l (+±+ht)_ ' ) 2 3 4

3-9 ¢. -pd A Leon-Garcia INSTRUCTOR'S SOLUTIONS MANU Probability, Statistic id JAL • astcs, andRandom Processesfor Electrical Enor, 8uneering - ? « -R coo{ ° tcah-{i -l¢19 c= o,%o T s { ttc fad zoo h- Ne» 1,c39 =e¥ P[x>+] = 1- PX<3] = t-c[vi +{( 1. - v-07 0325 a f l±r 2 'Zis nu,go6 tAt hcct 2 .d4A do fwa..t (ct tfp- h-{ 4),

A Leon-Garcia INSTRUCTOR'S SOLUTIONS MANUAL Probability, Statistics, and Random Processesfor Electrical Engineering

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5o.- - 37%: P[x>2]

t-Pl-l=% eLx >5] = PL=s -l, - s 3-10 7[ l- 0>2l ) = 1- PLx=2{= @ 5 o P[>o]= Plx=s] + r[x-) I !if) Y=0+2-2 p». /o {--I+2=l ?/% y--2+2=o /o Y--3+=-\ 'lo -I O ' lh <? P[y=2]= +/° It>·]= r er=0=l+? (3.18){¢ j& koMr 4 +as+.da .At} dsec°• %e 5 %' %' .,R +px<«1= z.6»-Ag=+ j°' 37° d-or -«st l= £«° c&7 sht set, epaa% ? 7x Loza<s bef- at so

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