Satistics

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



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, 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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