BinomialDistribution Formular PPT page 54

Example: PPT page 56

R Binomial Function

Density or point probability (d)

Cumulated probability distribution (p)

Quantiles (q)

Random generator (r)

Practice 1: Past Records, 0.08 probability that an online tretail order is fraudlent. Suppose we have 20 orders, Probbility no order is fraudulent?

Analysize the Problem: Triail -> Checking order ; Fraudelent or not? ;Whether we are sucess -> order is fraudulent; n = 20 trials; Pi = probability of success = 0.08; X = the number of fraudulent orders among the 20

Solution: P(X = 0) -> d; P(x<=a) = F(a) -> p; P(X = 0) is what we want!

R coding: PPT Page 63

dbinom(0, size = 20, prob = 0.08) # P( X = 0 )

Practice 2: Probability of 2 or more Fraudulent orders among the 20?

Solution: P(X>=2) = P(X>1) = 1 - F(1)

R Coding:

1-pbinom(1, size = 20, prob = 0.08)

Mean & Standard Deviation in PPT page 60

EV.Fraud = 20* 0.08
EV.Fraud

SD.Fraud = sqrt(20*0.08*(1-0.08))
SD.Fraud

Chebyshev Rule 75% of the time we will get success get 0 to 4 fraudulent orders

EV.Fraud - 2*SD.Fraud
EV.Fraud + 2*SD.Fraud