> <>; bjbjVV .&<<||$1333333$LWWl666161660{if60,6 6WW6| : Waiving DECS 433 vs. enrolling in DECS 445
This document provides a spartan outline of things that students who emerge from DECS 433 are supposed to have mastered. It cannot convey the full depth and richness of how these ideas should inform decision making in the face of uncertainty. This outline coupled with the sample waiver/diagnostic test should help you decide whether you should waive DECS 433 or enroll in 445.
If you feel that you are familiar with items 1-5 on this list and did well on the on-line test then you should consider waiving DECS 433.
If you are familiar with items 1 and 2 only and did well on the on-line test then you should consider taking the diagnostic test to qualify for DECS 445.
1. The Basics
The basic rules of probability:
Pr(A) + Pr(not-A) = 1; Pr(A and B) + Pr(A and not-B) = Pr(A)
Pr(A or B) = 1 Pr(not-A and not-B)
Pr(A or B) = Pr(A) + Pr(B) Pr(A and B)
The basic rules of conditional probability:
Definition: Pr(A|B) = Pr(A and B) / Pr(B)
Pr(A and B) = Pr(A)(Pr(B|A); when A and B are independent, Pr(A and B) = Pr(A)(Pr(B)
Pr(A and B and C) = Pr(A)(Pr(B|A)(Pr(C|A and B), and so on
Pr(A) = Pr(A|B1) ( Pr(B1) + + Pr(A|Bk) ( Pr(Bk), when B1, , Bk are disjoint and exhaustive
Bayes Rule, and Bayesian Updating
The basic rules of expectation:
E[aX+b] = a(E[X] + b
E[X+Y] = E[X] + E[Y]
E[X] = E[X|B1](Pr(B1) + + E[X|Bk](Pr(Bk), when B1,, Bk are disjoint and exhaustive
E[XY] = E[X](E[Y], if X and Y are independent
The basic rules of variability:
Definitions: Var(X) = E[X2] - (E[X])2 = E[(X-E[X])2]; StDev(X) = (Var(X)
Var(aX+b) = a2 Var(X); StDev(aX+b) = |a| StDev(X)
Var(X+Y) = Var(X) + Var(Y) + 2 Cov(X,Y)
Definition: Cov(X,Y) = E[XY] - E[X](E[Y] = E[ (X-E[X]) ( (Y-E[Y]) ]
Cov(aX+b,cY+d) = ac(Cov(X,Y)
Definition: Corr(X,Y) = Cov(X,Y) / ( StDev(X) ( StDev(Y) )
If X, X1, , Xn are independent and identically distributed:
E[X1++Xn] = n-E[X]
Var(X1++Xn) = n-Var(X); StDev(X1++Xn) = (n ( StDev(X),
Var( (X1++Xn) / n ) = Var(X) / n; StDev( (X1++Xn) / n ) = StDev(X) / (n
Special distributions:
Binomial: If n independent trials each have probability p of being a success, then the expected number of successes is np.
Geometric: If successive independent trials each have probability p of being a success, then the expected number of trials up to and including the first success is 1/p.
Normal: Fully determined by ( and (. Appears in many settings due to the Central Limit Theorem. Sums, differences, and linear transformations of normally-distributed random variables are normally distributed.
2. Spreadsheet skills
Spreadsheet functions
=IF, =MAX, =MIN
=AND, =OR
=SUM, =COUNT, =AVERAGE, =PRODUCT
=SUMIF, =COUNTIF
=SUMPRODUCT
=COMBIN, =FACT
=LOOKUP
=BINOMDIST, =NORMDIST, =NORMINV
=RAND, =RANDBETWEEN
Spreadsheet tools
Data Table command
Solver
Simulation skills
=IF(RAND()<=p,1,0) simulates an event with probability p
=NORMINV(RAND(),mu,sigma) simulates a normally-distributed random variable
Familiarity with accumulating the results of spreadsheet simulation
3. Decision Trees
Know how to construct and prune decision trees.
Determine the value of information.
4. Key concepts
The central limit theorem and its implications for risk management.
Knowing the difference between independent and dependent events why it matters.
Understand risk aversion and utility maximization
Understand that the policy ( that maximizes E[ f(X, () ] (i.e., a good policy) is not necessarily indeed, is usually not the policy ( that maximizes f(E[X], (). In words: The policy that would be optimal in the expected world is typically not the optimal policy.
Know what Adverse selection is and recognize when it is present.
5. Key applications
The role of diversification in risk management.
Valuing the option to both delay a decision as well as accelerate it.
Adverse selection in insurance, employment and procurement.
How variability impacts decisions about sourcing and retention for example.
When is information correctly aggregated?
+,:
-.MNUV}~
E
F
G
H
I
M
N
[
\
]
^
b
c
l
m
r
s
Ӽ⼴➥hwdh1@phwdh1@pH* jh1@phM/}h1@p6hwdh1@p56hQmFh1@p5 h1@p5h1@p56h<h1@p5h1@phxIh1@ph1@p5CJaJh6gr5CJaJ>+, 2
3
:_4o
%
:
)dgd1@pgd1@p$a$gd1@p
!"67!#$)*0123`cdhiyz~V»°°»hM/}h1@pH*hM/}h1@p56H*h1@p56hM/}h1@p56 jh1@phM/}h1@p6 jh1@phM/}h1@pH*h1@ph@{h1@p6hwdh1@p56?)]!`t:"8HRsgd1@p
&dPgd1@pxgd1@pgd1@pdgd1@pVW\]!"78
LNOPY\]>?VWXuvxڶᑶhGh1@p5h@rh1@p6 jnh1@phY?h1@p jph1@ph<h1@p5h<h1@p5hM/}h1@p56hu#h1@p56h1@p56 h1@p5hu#h1@p5 jsh1@ph1@p jmh1@p(
U(LM]#23
&dPgd1@pxx&dPgd1@px&dPgd1@pxgd1@pgd1@pgd1@p3tu;xgd1@pxxgd1@p
&dPgd1@p,1h/ =!"#$%^6866666662 0@P`p2( 0@P`p 0@P`p 0@P`p 0@P`p 0@P`p(8HX`~_HmH nH sH tH @`@NormalCJ_HaJmH sH tH DA DDefault Paragraph FontRiRTable Normal4
l4a(k (No ListPK![Content_Types].xmlj0Eжr(Iw},-j4 wP-t#bΙ{UTU^hd}㨫)*1P' ^W0)T9<l#$yi};~@(Hu*Dנz/0ǰ$X3aZ,D0j~3߶b~i>3\`?/[G\!-Rk.sԻ..a濭?PK!֧6_rels/.relsj0}Q%v/C/}(h"O
= C?hv=Ʌ%[xp{۵_Pѣ<1H0ORBdJE4b$q_6LR7`0̞O,En7Lib/SeеPK!kytheme/theme/themeManager.xmlM
@}w7c(EbˮCAǠҟ7՛K
Y,
e.|,H,lxɴIsQ}#Ր ֵ+!,^$j=GW)E+&
8PK!Ptheme/theme/theme1.xmlYOo6w toc'vuر-MniP@I}úama[إ4:lЯGRX^6؊>$!)O^rC$y@/yH*)UDb`}"qۋJחX^)I`nEp)liV[]1M<OP6r=zgbIguSebORD۫qu gZo~ٺlAplxpT0+[}`jzAV2Fi@qv֬5\|ʜ̭NleXdsjcs7f
W+Ն7`gȘJj|h(KD-
dXiJ؇(x$(:;˹!I_TS1?E??ZBΪmU/?~xY'y5g&/ɋ>GMGeD3Vq%'#q$8K)fw9:ĵ
x}rxwr:\TZaG*y8IjbRc|XŻǿI
u3KGnD1NIBs
RuK>V.EL+M2#'fi~Vvl{u8zH
*:(W☕
~JTe\O*tHGHY}KNP*ݾ˦TѼ9/#A7qZ$*c?qUnwN%Oi4=3ڗP
1Pm\\9Mؓ2aD];Yt\[x]}Wr|]g-
eW
)6-rCSj
id DЇAΜIqbJ#x꺃6k#ASh&ʌt(Q%p%m&]caSl=X\P1Mh9MVdDAaVB[݈fJíP|8քAV^f
Hn-"d>znǊ ة>b&2vKyϼD:,AGm\nziÙ.uχYC6OMf3or$5NHT[XF64T,ќM0E)`#5XY`פ;%1U٥m;R>QDDcpU'&LE/pm%]8firS4d7y\`JnίIR3U~7+#mqBiDi*L69mY&iHE=(K&N!V.KeLDĕ{D vEꦚdeNƟe(MN9ߜR6&3(a/DUz<{ˊYȳV)9Z[4^n5!J?Q3eBoCMm<.vpIYfZY_p[=al-Y}Nc͙ŋ4vfavl'SA8|*u{-ߟ0%M07%<ҍPK!
ѐ'theme/theme/_rels/themeManager.xml.relsM
0wooӺ&݈Э5
6?$Q
,.aic21h:qm@RN;d`o7gK(M&$R(.1r'JЊT8V"AȻHu}|$b{P8g/]QAsم(#L[PK-![Content_Types].xmlPK-!֧6+_rels/.relsPK-!kytheme/theme/themeManager.xmlPK-!Ptheme/theme/theme1.xmlPK-!
ѐ' theme/theme/_rels/themeManager.xml.relsPK]
&
V)3
8@0(
B
S ? OLE_LINK1
ELZ^X\ac"%),-18;BGHLTY]`hkqt|/1gitw}emk (a'808^8`0o(.
^`hH.
pLp^p`LhH.
@@^@`hH.
^`hH.
L^`LhH.
^`hH.
^`hH.
PLP^P`LhH.k ( 1@p6gr@`@UnknownG*Ax Times New Roman5Symbol3.*Cx ArialACambria Math"qh&&WZ
WZ
!24d
3QHX)?tw02The basic rules of probability:BobMichael SaraOh+'0Px
$08@H The basic rules of probability:BobNormal.dotmMichael Sara2Microsoft Office Word@@Qif@QifWZ
՜.+,0hp
Home The basic rules of probability:Title
!"#$%&'()*,-./012456789:=Root Entry Fjif?Data
1TableWordDocument.&SummaryInformation(+DocumentSummaryInformation83CompObjy
F'Microsoft Office Word 97-2003 Document
MSWordDocWord.Document.89q