NRI INSTITUTE OF TECHNOLOGY (Approved by AICTE, New Delhi: Affiliated to JNTUK, Kakinada POTHAVARAPPADU (!, (via N"nna, A#iripalli A#iripalli ($, ($ , Kri%hna Di%tri&t, A'' A'', IN: )*+ *+*, h: -.)./0*1222 3eb%ite: 3e b%ite: nri#ro"pof&olle#e%'&o4 e/4ail: nri#ro"pof&olle#e%5#4ail'&o4 DEA6T$ENT 78 E9ECT67NIC AND C7$$UNICATI7N EN;INEE6IN; N6IIT<=')'+<6C N6IIT<=')'+<6C 1
LESSON PLAN Depart4ent: ECE Na4e of fa&"lty: T.SUMALATHA
e4e%ter e4e%t er < >ear: >ear: II/II B-SEC
De%i#nation: ASST. PROFESSOR
Na4e of the %"b?e&t: RANDOM VARIABLES & STOCHASTIC PROCESSES
No of NRI INSTITUTE OF TECHNOLOGY No of S.NO TOPIC C!la"#$e (Approved by AICTE, New Delhi: Affiliated to JNTUK, Kakinada Classes Classes POTHAVARAPPADU (!, (via N"nna, A#iripalli ($, Kri%hna Di%tri&t, A'', IN: )*+ *+*, h: -.)./0*1222 3eb%ite: nri#ro"pof&olle#e%'&o4 I UNIT % THE RANDOM VARIABLE e/4ail: nri#ro"pof&olle#e%5#4ail'&o4 DEA6T$ENT 78 E9ECT67NIC AND C7$$UNICATI7N EN;INEE6IN; +'+ Introd"&tion + +
+'*
Definition of a 6and o4 !ariable, Condition% for a 8"n&tion to be a 6ando4 !ariable
+
*
+'0
Di%&rete and Contin"o"%, $i@ed 6ando4 !ariable%
+
0
+'1
Di%trib"tion f"n&tion and it% ropertie%, roble4%
+
1
+')
Den%ity f"n&tion% and it% ropertie%, roble4%
+
)
+'.
ino4ial, oi%%on Di%trib"tion and Den%ity f"n&tion%
+
.
+'=
Unifor4 ,E@ponential, 6aylei#h Di%trib"tion and Den%ity f"n&tion% ;a"%%ian 6ando4 !ariable, roble4% on ;a"%%ian 6and o4 !ariable%
+
=
+
-
+'2
Conditional Di%trib"tion, Conditional Den%ity and it% ropertie%
+
2
+'+
6E!I7U 679E$
+
+
+
++
+
+*
*'0
Introd"&tion, E@pe&ted !al"e of a 6ando4 !ariable 8"n&tion of a 6ando4 !ariable, $o4ent% abo"t the 7ri#in and roble4% Central $o4ent%, roble4% on Central $o4ent%,
+
+0
*'1
!arian&e and kew, roble4% on !arian&e and kew
+
+1
*')
Cheby&hevB% Ine"ality
+
+)
*'.
Chara&teri%ti& 8"n&tion and it% ropertie%
+
+.
*'=
$o4ent ;eneratin# 8"n&tion and it% ropertie%
+
+=
*'-
Tran%for4ation% of a 6ando4 !ariable: $onotoni& Tran%for4ation% for a Contin"o"% 6ando4 !ariable
+
+-
*'2
Non $onotoni& Tran%for4ation% for a Contin"o"% 6ando4 !ariable
+
+2
*'+
6E!I7U 679E$
+
*
+'-
II
*'+ *'*
UNIT ' OPERATION ON ONE RANDOM VARIABLE ( E)PECTATIONS
III
UNIT * +A, MULTIPLE RANDOM VARIABLES
0'+
!e&tor 6ando4 !ariable%, Joint Di%trib"tion 8"n&tion and it% ropertie%
+
*+
0'*
Joint Den%ity 8"n&tion and it% ropertie%
+
**
0'0
$ar#inal Di%trib"tion 8"n&tion%, roble4%
+
*0
0'1
Conditional Di%trib"tion and Den%ity f"n&tion%
+
*1
0')
tati%ti&al Independen&e, "4 of Two 6ando4 !ariable%
+
*)
0'.
"4 of everal 6ando4 !ariable% and roble4%
+
*.
0'=
Central 9i4it Theore4, Une"al Di%trib"tion, E"al Di%trib"tion%
+
*=
III-B
+B, OPERATIONS ON MULTIPLE RANDOM VARIABLES
0'-
Introd"&tion
+
*-
0'2
Joint $o4ent% abo"t the 7ri#in, roble4%
+
*2
0'+
Joint Central $o4ent%, roble4%
+
0
0'++
Joint Chara&teri%ti& 8"n&tion%, roble4%
+
0+
0'+*
Jointly ;a"%%ian 6ando4 !ariable%: Two 6ando4 !ariable% &a%e
+
0*
0'+0
N 6ando4 !ariable &a%e, ropertie%
+
00
NRI INSTITUTE OF TECHNOLOGY (Approved by AICTE, New Delhi: Affiliated to JNTUK, Kakinada POTHAVARAPPADU (!, (via N"nna, A#iripalli ($, Kri%hna Di%tri&t, A'', IN: )*+ *+*, h: -.)./0*1222 3eb%ite: nri#ro"pof&olle#e%'&o4 e/4ail: nri#ro"pof&olle#e%5#4ail'&o4 DEA6T$ENT 78 E9ECT67NIC AND C7$$UNICATI7N EN;INEE6IN;
TE)T BOOS •
robability, 6ando4 !ariable% 6ando4 i#nal rin&iple% / eyton ' eeble%, T$F, 1 th Edition, *+'
•
robability, 6ando4 !ariable% and to&ha%ti& ro&e%%e% G Athana%io% apo"li% and ' Unnikri%hna illai, FI, 1th Edition, **'
REFERENCES •
robability Theory and to&ha%ti& ro&e%% G rabhakara 6ao, 7@ford Univer%ity re%%'
•
robability and 6ando4 ro&e%%e% with Appli&ation to i#nal ro&e%%in# G Fenry tark and John 3' 3ood%, ear%on Ed"&ation, 0rd Edition'
•
robability $ethod% of i#nal and y%te4 Analy%i%' ;eor#e 6' Cooper, Clave D' $C ;ille4, 7@ford, 0rd Edition, +222'
•
tati%ti&al Theory of Co44"ni&ation / '' E"#ene Havier, New A#e "bli&ation%, *0'
Peae0 Fa1l"2 / Da"e
Ve#f#e0 HOD/Da"e
