Exercise 1
100%
P
S
1/10000=0.01%
9999/10000=99.99%
0%
Pc
1%
P
99%
Pc
Sc
S= Have swine Flu
Sc = Do not have swine flu
P = Positive
Pc = Not positive
Exercise 2
100%
P
S
1/200=0.5%
199/200=99.5%
0%
Pc
1%
P
99%
Pc
Sc
S= Have swine Flu
Sc = Do not have swine
Investment
A
B
C
D
Mean
2.50%
4.50%
6%
10%
St dev.
0.10%
0.50%
1%
5%
Estimating Mean and Standard Deviation of Stock Returns
Historical data
Month
0
1
2
3
4
5
6
7
8
9
10
11
12
Closing
$25.00
$24.70
$23.70
$22.90
$22.81
$22.89
$22.56
$23.94
$24.37
$24.99
$
Continuous Probability Distribution
Uniform Probability Distribution
Normal Probability Distribution
Standard Normal Probability Distribution
NORM.DIST Excel function
NORM.INV Excel function
NORM.S.DIST Excel function
NORM.S.INV Excel function
Exponential
restaurant
Parameters
Nb seats
Mean Revenue/customer
stdev
Proba show up
badwill
75
100
25
0.8
500
Decision
Number reservations
77
Int. Calculations
60
Nb show up
Nb customers accepted
Nb customers not accepted
Result
Margin
60
0
5,910.02
Page 1
restauran
Topics
Notes
Adding Sample Points to Find Probability
Combinations and Permutations
Adding Laws for Probability
Multiplying Laws for Probability
Comprehensive Example From Cross Tabulated Tables
Bayes' Theorem
Sheet Name (link to jump)
Notes
ALL SP
ALL SP
Topics
Random Variables
Discrete Random Variables
Continuous Random Variables
Build Discrete Probability Distributions
Expected Value for a Discrete Random Variables
Variance and Standard Deviation for a Discrete Random Variables
Binomial Experiment & Bin
Test about one mean
The beta coefficient of a stock is a measure of the stocks volatility (or risk) relative to the ma
beta coefficients greater than 1 generally bear greater risk (more volatility) than the market, w
coefficients less than 1 are less risk
SE
z calc
z crit
2
1.75
1.959964
z calc < z crit so H0 is not rejected
p-value
0.080118
p-value > alpha so don't reject H0
Using R
>Zcalc <- (403.5-400)/(10/sqrt(2
> Zcalc
[1] 1.75
> pval<-2*(1-pnorm(Zcalc)
> pval
[1] 0.08011831
g R
c <- (403.5-400)/(10/s
Session 2
Probability and
Probability Distributions
Probability
And
Probability
Distributions
Basic
probability
concepts
Random
Variables
Session outline
Basic probability concepts
Random variables and Probability
distributions
Association
2/29
Probabil
n
27
73
19
16
64
28
31
90
60
56
31
56
22
18
45
48
17
17
17
91
92
63
50
51
69
26
17
28
H0
h1
mu <= 35
mu > 35
Mean
44.25926
St Dev
24.93004
Se
4.797789
z calc
1.929901
p-value
0.032299
To calculate this rejection area
1-NORM.S.DIST(2.02,TRUE)
1.929901
n
x
Today, you are an assembly line manager. You have two products under your supervision (dress and shoes).
You are trying to maximize your profit. However, because of factory size, you can not produce more than 500 units of a spe
In addition, you are limite
SLIDE 8
X
P(X)
Number of trial n
Probability of success p
Slide 10
Two ways to do it :
P(X<= 3)
P(X>2)
0
1
2
3
0.168 0.360 0.309 0.132
5
0.3
0.9692
0.1631
0.9692
0.1631
4
5
0.028 0.002
Slide 22
1.P(0< Z <1.5)
2.P(1< Z < 2)
3.P(-1< Z < 0)
4.P(-2 < Z < 2)
5
EX 1
Tha American Automobile Associaition (AAA) reports that the average daily meal and lodging costs
for a family of 4 members is 213$ with a standard deviation equal to 15$
Given a sample of 49 families:
1/ Describe the sampling distribution of xbar, th
Problem 1
Peter Biggs wants to know how growth managers performed last year. Biggs assumes that
the population cross-sectional standard deviation of growth manager returns is 6 percent
and that the returns are independent across managers.
A. How large a r
You are a manufacter of chocolate.
You have to choose between 3 different type of chocolate to produce and sell from
Dark chocolate, Milk chocolate and white chocolate.
Demand for the three type of chocolate is given below (in bar of chocolate)
Dark:
500
IQ
1 John
2 Bob
3 Tversky
4 Kahneman
5 Tony
6 Selma
7 Hayek
8 Dresden
9 Lucie
10 Ted
English Test score
15
25
35
45
55
65
75
85
95
105
35
45
83
65
92
85
95
105
84
120
Average IQ
Average test score
STDEV IQ
STDEV test score
60
80.9
30.276503541
26.05741523
Additional material: not required at
all for the final quiz
This material may be useful to answer the interrogation you will have during the year concerning the
link between the simple regression and the capital asset pricing model. It is well beyond the
Binomial distribution
1)
2)
Suppose you have an urn filled with 40 green ball and 60 red ball. You pick 5 balls with
replacement. You want to know the probability of picking a green ball a certain
number of time.
Define the random variable, X.
What are po
I]
You go to see the doctor about an ingrowing toenail. The doctor selects you at random to have
a blood test for swine flu, which for the purposes of this exercise we will say is currently suspected
to affect 1 in 10,000 people in France. The test is 99%
Bayes Theorem
I]
Alice has two coins in her pocket, a fair coin (head on one side and tail on the other side) and
picks one at random from her pocket, tosses it and obtains head. What is the probability that
P(F|H)= P(FnH)/(P(H)
0.3333333333
P(F)
P(H2)
0.
The disadvantage of the mean as an indicator of central
tendancy is that :
Eye Color (blue, black or green) is a ? variable
it is sensible to extreme values
nominal
Normal Distribution
I]
Let Z be a random variable having a standard normal distribution.
W
Cookies I
V
75%
B1
50%
25%
50%
50%
C
V
B2
50%
C
B1 = Bowl 1
B2 = Bowl 2
V = Vanilla cookie
C = Chocolat cookie
Cookies II
V
80%
B1
50%
20%
60%
50%
C
V
B2
40%
C
B1 = Bowl 1
B2 = Bowl 2
V = Vanilla cookie
C = Chocolat cookie
Gene testing
P
90%
S
1%
10%
9.6%
Bayes Theorem additionnal exercises
I]
Suppose there are two bowls of cookies. Bowl 1 contains 30 vanilla cookies and 10 chocolate cookies. Bowl 2 co
Now suppose you choose one of the bowls at random and, without looking, select a cookie at random.
The co
Fair coin
H
50%
F
50%
50%
100%
50%
T
H
H2
0%
T
F = Fair coin
H2 = 2 headed coin
H = Head
T = Tail
Balls of different colours
R
50%
U1
50%
50%
B
R
30%
50%
U2
70%
B
Marie Wedding
Ps
90%
nR
360/365= 98.63%
10%
Pr
Ps
10%
5/365= 1.37%
R
90%
Pr
Ps = Predicted S
EMPLOYEES DATABASE
Following are records of a sample of employees of a company
ID
SALARY
GENDER
AGE
1
2
21,894.40
38,539.20
F
M
42
54
EXPERIENCETRAINING LEVEL
3
10
B
B
3
4
38,177.60
38,738.40
M
M
47
47
10
1
A
B
5
6
36,481.60
35,226.40
M
M
44
42
5
10
Cans Exericse
X
Mean
alpha
n
st dev
403.5
400
5%
25
10
st error
2
Z calc
1.75
Z crit
1.9599639845
Z calc > z crit No H0 rejection
p-value
0.0801183137
P-value>alpha No H0 rejection
Hypothesis Testing
Ho
H1
2000g
no 200g
st dev
Mean
n
Sample mean
18
200
36
SUNRISE RICE
Suppose the net weight (x) of 20kg bag Sunrise rice is normally distributed. With mean = 20kg and st.deviation = 0.4kg
Case (a): If you purchase 1 bag, find P(X<19.5)
0.10565
Case (b): If you purchase 9 bags, find P(X bar < 19.5)
VOTING INTEN
Bayes Theorem
P( A1 | B ) =
I]
Alice has two coins in her pocket, a fair coin (head on one side and tail on the other side) and
She picks one at random from her pocket, tosses it and obtains head. What is the probability
fair coin?
II]
There are two urns