binomial experiments
TRANSCRIPT
Defi
nitio
nBinomial Experiment:
Defi
nitio
nBinomial Experiment:
►experiment is repeated for fixed number of trials
Defi
nitio
nBinomial Experiment:
►experiment is repeated for fixed number of trials
► two possible outcomes:
Defi
nitio
nBinomial Experiment:
►experiment is repeated for fixed number of trials
► two possible outcomes:
► Success or Failure
Defi
nitio
nBinomial Experiment:
►experiment is repeated for fixed number of trials
► two possible outcomes:
► Success or Failure
► probability of success is constant
Defi
nitio
nBinomial Experiment:
►experiment is repeated for fixed number of trials
► two possible outcomes:
► Success or Failure
► probability of success is constant
► x counts the number of successful
trials
Notation
Symbol
Description
n the number of times a trial is repeated
Notation
Symbol
Description
n the number of times a trial is repeated
p the probability of success
Notation
Symbol
Description
n the number of times a trial is repeated
p the probability of success
q the probability of failure
Notation
Symbol
Description
n the number of times a trial is repeated
p the probability of success
q the probability of failure
x the number of successes out of n trials
Exam
ple
You roll a pair of 6-sided dice 5 times, and note whether or not you rolled a pair of doubles like(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)
Exam
ple
You roll a pair of 6-sided dice 5 times, and note whether or not you rolled a pair of doubles like (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)
► n =5 (you rolled the dice 5 times)► A binomial experiment has a fixed
number of trials
Exam
ple
You roll a pair of 6-sided dice 5 times, and note whether or not you rolled a pair of doubles like (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)
► n =5 (you rolled the dice 5 times)► A binomial experiment has a fixed
number of trials
Exam
ple
You roll a pair of 6-sided dice 5 times, and note whether or not you rolled a pair of doubles like (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)
► n =5 (you rolled the dice 5 times)► A binomial experiment has a fixed
number of trials
Exam
ple
You roll a pair of 6-sided dice 5 times, and note whether or not you rolled a pair of doubles like (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)
► n =5 (you rolled the dice 5 times)► A binomial experiment has a fixed
number of trials
Exam
ple
You roll a pair of 6-sided dice 5 times, and note whether or not you rolled a pair of doubles like (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)
► n =5 (you rolled the dice 5 times)► A binomial experiment has a fixed
number of trials
Exam
ple
You roll a pair of 6-sided dice 5 times, and note whether or not you rolled a pair of doubles like (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)
► n =5 (you rolled the dice 5 times)► A binomial experiment has a fixed
number of trials► p = 6/36, the probability of success
► A binomial experiment has a fixed rate of success
Exam
ple
You roll a pair of 6-sided dice 5 times, and note whether or not you rolled a pair of doubles like (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)
► n =5 (you rolled the dice 5 times)► A binomial experiment has a fixed
number of trials► p = 6/36, the probability of success
► A binomial experiment has a fixed rate of success
► q = 30/36, the probability of failure► q = 1-p
Exam
ple
You roll a pair of 6-sided dice 5 times, and note whether or not you rolled a pair of doubles like (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)
► n =5 (you rolled the dice 5 times)► A binomial experiment has a fixed
number of trials► p = 6/36, the probability of success
► A binomial experiment has a fixed rate of success
► q = 30/36, the probability of failure► q = 1-p
► x = {0, 1, 2, 3, 4, 5}, the number of successes out of n trials
Revi
ewBinomial experiments:
Revi
ewBinomial experiments:
• fixed number of trials, n
Revi
ewBinomial experiments:
• fixed number of trials, n
• Probability of success, p, is the same for all trials
Revi
ewBinomial experiments:
• fixed number of trials, n
• Probability of success, p, is the same for all trials
• probability of failure, q, is the compliment of p (q = 1 – p).
Revi
ewBinomial experiments:
• fixed number of trials, n
• Probability of success, p, is the same for all trials
• probability of failure, q, is the compliment of p (q = 1 – p).
• x is the number of successes out of n trials, x = 0, 1, 2, 3, …, n