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Lecture 8

# Lecture 8 (week 9)

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Ryerson University

Quantitative Methods

QMS 102

Clare Chua

Fall

Description

Key Answers
Topics that will be tested in Page 241
Quiz 2:
5.10) E(X)=$80,000
5.11a)
Discrete Probability # years X P(X)
1 $2.00 0.5
Binomial Probability
2 3.50 0.2
Poisson Probability 3 4.50 0.2
5 6.50 0.1
Normal Probability
5.11b) $406.25 Q5.14) Tire C
5.12a) Project 3
b) Project 3 Q 5.15) Order 11 units
5.13) Country C
Which of the above probability
distributions are for a discrete
random variable? Continuous?
Discrete Continuous
Binomial Probability Distribution
Binomial Normal
Poisson Inverse
Normal
Central Limit
Theorem
Addicreterandom variabe may assume either a finite number How to differentiate between
of values or an infinite sequence of values.
discrete and continuous random
Discrete variables?
CONTINUOUS
Random Variables DISCRETE
The observation can be The observation can be
counted measured
Example: the number of EExamplleTiime ((iin
students who drive to seconds) is measured and
FINITE INFINITE school not counted.
Number of values Number of values What is the probability What is the probability
that at most 110 students that the download time for
will drive to school? a home page on a Web
browser is between 7 and
10 seconds?
1
www.notesolution.com Discrete Random Variable
Examples: Finite/Infinite number
values
Experiment Random Possible
What is a Binomial Probability
Variable Value s
Maake 1100sales calslls# Saless 0,1,,2,, .1000.,, 1 Distribution?
Fiiniitte
Inspect 70 radios # Defective 0, 1, 2, ..., 70 Number
values
Answer 33 questions # Correct 0, 1, 2, ..., 33
Count cars at toll # Cars 0, 1, 2, ..., B
between 11:00 & 1:00 arrivin g Infinite
Number
values
Characteristics of the Binomial
Distribution
Summary: Three pieces of info
1. The experiment consists of a sequence of n
identical trials (repetitions).
2. Each trial has only one of the two possible mutually 1. Sequence of n identical trials / A sample of n
exclusive outcomes, success or a failure. Two items are selected from a large population
outcomes, success and failure, are possible on each 2. Constant Probability (!) for each Trial
trial. eg..Probabiiy ofgettnga aiillhee ame each
time we toss the coin and each light bulb has the
3. The probability of each outcome does not change same probability of being defective
from trial to trial.
4. The trials are independent, thus we must sample with 3. Each trial has 2 outcomes
replacement. Success (desired outcome) or failure
The random variable that we are interested in is, X= # of successes
To calculate the probability that X takes on a
Number of successesin a sample specific value we use the Binomial Probability
of n observations (trials) Distribution Function
X= # of successes
Use the CASIO calculator to obtain the
What is the Binomial Probability Binomial Probability
See Handout on CASIO Calculator Lesson 3 :
Distribution Function? Binomial and Poisson page 250
n! x n
x Using the CASIO calculator
P ( x) 5 (1
)
x!(
)! STAT F5(DIST) F5(BINM) F1(Bpd)
P(X=x) = probability that x successes given a knowledge of Then select the following options
n and !
You will see: Binomial P.D
X = number of successes in Data : Variable
sample, (X = 0, 1, 2, ..., n) X :
Numtrial :
5 = probability of each success P :
n = sample size Save Res: None
Execute
2
www.notesolution.comBpd and Bcd functions Use the CASIO calculator to obtain the
The Casio calculator has 2 Binomial Probability Binomial Probability
functions programmed into its memory. Experiment: Toss 1 coin 6 times in a row..
These are: Whats the probability of getting 2 tails?
See Handout on CASIO Calculator
1) Bpd stands for Binomial Probability Distribution.
This function calculators a Binomial Probability of the form: Lesson 3 : Binomial and Poisson page 250
X= #offaiillssTTAT FF5(DIST))F5(BINM)) F1(Bppd))
P((X= #)) n = 6 Then select the following options

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