The statistics document is to further your understanding, as this is a very difficult module to understand, let alone achieve a pass. Everyone I know, including me, failed the first time around, so it's very important to get a grip on this module.
Greenwich University
Asef Khan
Economics :Statistics for Economics and Finance. Continuous Probability Distributions
Tutor: Alex
13.2.2023
ANNOUNCEMENTS
Matthew -current Masters student- alerting you to Economics conference 25th Feb.
Rethinking Economics
Conferences started after 2008- economics as a discipline to understand the crisis,
important for him to meet with people who are interested in discussion
Lecturers from various professional backgrounds /universities. FT financial times and
other think tanks will be present
Check on Eventbrite and register
Alex -- now cost of living crisis > period of clash of economic ideas / battle of ideas so
it’s good to debate different economic approaches> use the Moodle as forum for
discussion too
MATERIAL FROM LAST WEEK-BINOMIAL DISTRIBUTION
Last week discussed binomial distribution and case relating to it.Will use as comparison for
this lecture.
Formula for binomial distribution
Probability( P) of a number of successes( x =3) in a number of trials (n=10)
e.g. P= 0.5 with 10 trials and 5 successes
Probability distributions- Bernoulli Distribution. See formula from previous week.
Formula probability distribution
See slide for exact formula details
Formula: 0.5 (prob of successes)to power of 5 ( no of successes) x 0.5 (probability of
failure) to power of n (10 trials – 5 successes x binomial coefficient)
This will indicate the number of ways to have 5 successes in 10 trials if you don’t care
about the order of success of failure > e.g., could have success, success, failure and 2 more
successes or any other combination.
Read up further in textbook if any confusion.
Applying the binomial distribution- example
Police seize 496 packets of white powder, presumably cocaine
4 of packets were tested and all were positive for cocaine
Police selected 2 random packets from 496 and sold on street by undercover police
officers
Between sale and arrest, the buyer disposed of the evidence
1
, Greenwich University
Asef Khan
Economics :Statistics for Economics and Finance. Continuous Probability Distributions
Tutor: Alex
13.2.2023
Buyer’s attorney argued in court that police selected two random packets from 496
having previously tested 4 packets> how do we know police sold cocaine? Buyers
just bought packets of white powder, no proof of crime. Lawyer- some of police
packets have cocaine but not all tested so some might not have cocaine
if 496 packets, then the probability of first selecting 4 that contain cocaine and 2
that do not is maximised if 331 packets contain coke and 165 do not
If 331 contained coke and 165 did not= 67% probability of picking random pack
that contains cocaine
Question- what is the probability that of the 496 packets you first choose 4 that do
contain coke, then choose 2 that don’t contain cocaine
Prob of choosing the first four cocaine packets( 4 successes) with probability of 67%
in 4 trials and probability of failure of 33%=around 20%
Prob of then choosing two packets that don’t contain cocaine i.e. 0 successes in 2
trials with same probability of success and failure
Joint probability of those two events ( assuming statistically independent) = 2.2%
Judge agreed that 2.2 % prob was not enough to prove the offence
Key- note the shape of Binomial distribution in probability distribution. See graph slide
N trials with prob of success of 10%
Vertical axis=probability of obtaining 0,1,2 or 3 etc of successful trials; horizontal
axis- probability of gaining a specific number of successes
Prob distribution – low prob of success up to 0.1 ; higher probability of 0 successes
at 5 trials to getting 2/3 successes at 5 trials( 50% prob of success)
Key- relevant to continuous distribution formulas
Mean and standard deviation and how to calculate this relates to formula for
Bernoulli distribution discussed last week.
Binomial distribution tables
In tutorials you’ll be asked to apply binomial distribution tables
Tables calculate the probability of number of successes out of a number of trials
He will also discuss how to apply Excel but tables are a useful alternative to formula
Tables show X no of successes and p the probability of success. e.g. 2 successes in 3
trials with prob of success of 25%. Use columns to find answer- here the probability
= 40.6%. Same as if you had worked through the formula.
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