Geometric And Poisson Probability DistributionsSuppose we have an experiment in which we repeat binomial trials until we get our first success, and then we stop. Let be the number of the trial on which we get our first success. IN this context, is not a fixed number. This is a GEOMETRIC PROBABILITY DISTRIBUTION.

Geometric And Poisson Probability DistributionsSuppose we have an experiment in which we repeat binomial trials until we get our first success, and then we stop. Let be the number of the trial on which we get our first success. IN this context, is not a fixed number. This is a GEOMETRIC PROBABILITY DISTRIBUTION.

where - is the number of the trial we get our first success

- is the probability of success on each trial

Also : AND

Geometric And Poisson Probability Distributions

where - is the number of the trial we get our first success

- is the probability of success on each trial

Also : AND EXAMPLE : A welding robot in an automobile plant looks for a small magnetic dot

to perform a spot weld. The robot has an 85% success rate for finding

the dot. If it can not find the dot on the first try, it is programmed to

search again. a) Find the probability of success on attempts

Geometric And Poisson Probability Distributions

where - is the number of the trial we get our first success

- is the probability of success on each trial

Also : AND EXAMPLE : A welding robot in an automobile plant looks for a small magnetic dot

to perform a spot weld. The robot has an 85% success rate for finding

the dot. If it can not find the dot on the first try, it is programmed to

search again. a) Find the probability of success on attempts

Geometric And Poisson Probability Distributions

where - is the number of the trial we get our first success

- is the probability of success on each trial

Also : AND EXAMPLE : A welding robot in an automobile plant looks for a small magnetic dot

to perform a spot weld. The robot has an 85% success rate for finding

the dot. If it can not find the dot on the first try, it is programmed to

search again. a) Find the probability of success on attempts

Geometric And Poisson Probability Distributions

where - is the number of the trial we get our first success

- is the probability of success on each trial

Also : AND EXAMPLE : A welding robot in an automobile plant looks for a small magnetic dot

to perform a spot weld. The robot has an 85% success rate for finding

the dot. If it can not find the dot on the first try, it is programmed to

search again. a) Find the probability of success on attempts

Geometric And Poisson Probability Distributions

where - is the number of the trial we get our first success

- is the probability of success on each trial

Also : AND EXAMPLE : A welding robot in an automobile plant looks for a small magnetic dot

to perform a spot weld. The robot has an 85% success rate for finding

the dot. If it can not find the dot on the first try, it is programmed to

search again.

b) The assembly line moves so fast, the robot only has 3 seconds before

the dot is out of range. What is the probability that the robot will find

the dot before it is out of range ?

Geometric And Poisson Probability Distributions

where - is the number of the trial we get our first success

- is the probability of success on each trial

Also : AND EXAMPLE : A welding robot in an automobile plant looks for a small magnetic dot

to perform a spot weld. The robot has an 85% success rate for finding

the dot. If it can not find the dot on the first try, it is programmed to

search again.

b) The assembly line moves so fast, the robot only has 3 seconds before

the dot is out of range. What is the probability that the robot will find

the dot before it is out of range ?

Geometric And Poisson Probability Distributions

where - is the number of the trial we get our first success

- is the probability of success on each trial

Also : AND EXAMPLE : A welding robot in an automobile plant looks for a small magnetic dot

to perform a spot weld. The robot has an 85% success rate for finding

the dot. If it can not find the dot on the first try, it is programmed to

search again.

b) The assembly line moves so fast, the robot only has 3 seconds before

the dot is out of range. What is the probability that the robot will find

the dot before it is out of range ?

Geometric And Poisson Probability Distributions

where - is the number of the trial we get our first success

- is the probability of success on each trial

Also : AND EXAMPLE : A welding robot in an automobile plant looks for a small magnetic dot

to perform a spot weld. The robot has an 85% success rate for finding

the dot. If it can not find the dot on the first try, it is programmed to

search again.

c) Find the mean and standard deviation

Geometric And Poisson Probability Distributions

where - is the number of the trial we get our first success

- is the probability of success on each trial

Also : AND EXAMPLE : A welding robot in an automobile plant looks for a small magnetic dot

to perform a spot weld. The robot has an 85% success rate for finding

the dot. If it can not find the dot on the first try, it is programmed to

search again.

c) Find the mean and standard deviation

Geometric And Poisson Probability Distributions

where - is the number of the trial we get our first success

- is the probability of success on each trial

Also : AND EXAMPLE : A welding robot in an automobile plant looks for a small magnetic dot

to perform a spot weld. The robot has an 85% success rate for finding

the dot. If it can not find the dot on the first try, it is programmed to

search again.

c) Find the mean and standard deviation

Geometric And Poisson Probability Distributions

POISSON DISTRIBUTIONA binomial distribution where as the number of trials gets larger, the probability of success gets smaller.

Geometric And Poisson Probability Distributions

POISSON DISTRIBUTIONA binomial distribution where as the number of trials gets larger, the probability of success gets smaller.

Let ( Greek letter lambda ) be the mean number of successes over time, volume, area, and so forth. Let be the number of successes ( in a corresponding interval of time, volume, area, and so forth. The probability of success in the interval is :

where = 2.7183 ( natural log )

Geometric And Poisson Probability Distributions

POISSON DISTRIBUTIONA binomial distribution where as the number of trials gets larger, the probability of success gets smaller.

Let ( Greek letter lambda ) be the mean number of successes over time, volume, area, and so forth. Let be the number of successes ( in a corresponding interval of time, volume, area, and so forth. The probability of success in the interval is :

where = 2.7183 ( natural log )

ALSO : AND

Geometric And Poisson Probability Distributions

POISSON DISTRIBUTION

where = 2.7183 ( natural log ).

AND

EXAMPLE : What if the rate of catching fish on a certain lake is 0.667 per hour. You

decide to fish the lake for 7 hours. Find a probability distribution for

the number of fish you catch in 7 hours.

Geometric And Poisson Probability Distributions

POISSON DISTRIBUTION

where = 2.7183 ( natural log ).

AND

EXAMPLE : What if the rate of catching fish on a certain lake is 0.667 per hour. You

decide to fish the lake for 7 hours. Find a probability distribution for

the number of fish you catch in 7 hours.First we must adjust the expected success rate for the 7 –

hour interval :

Geometric And Poisson Probability Distributions

POISSON DISTRIBUTION

where = 2.7183 ( natural log ).

AND

EXAMPLE : What if the rate of catching fish on a certain lake is 0.667 per hour. You

decide to fish the lake for 7 hours. Find a probability distribution for

the number of fish you catch in 7 hours.First we must adjust the expected success rate for the 7 –

hour interval :

Then :

Geometric And Poisson Probability Distributions

POISSON DISTRIBUTION

where = 2.7183 ( natural log ).

AND

EXAMPLE : What if the rate of catching fish on a certain lake is 0.667 per hour. You

decide to fish the lake for 7 hours. Find a probability distribution for

the number of fish you catch in 7 hours.First we must adjust the expected success rate for the 7 –

hour interval :

Then :

Find the probability of catching 2 fish in 7 hours

Geometric And Poisson Probability Distributions

POISSON DISTRIBUTION

where = 2.7183 ( natural log ).

AND

EXAMPLE : What if the rate of catching fish on a certain lake is 0.667 per hour. You

decide to fish the lake for 7 hours. Find a probability distribution for

the number of fish you catch in 7 hours.First we must adjust the expected success rate for the 7 –

hour interval :

Then :

Find the probability of catching 2 fish in 7 hours

Geometric And Poisson Probability Distributions

Then :

Find the probability of catching 3 or more fish. [ ]

Geometric And Poisson Probability Distributions

Then :

Find the probability of catching 3 or more fish. [

Geometric And Poisson Probability Distributions

Then :

Find the probability of catching 3 or more fish. [

Geometric And Poisson Probability Distributions

Then :

Find the probability of catching 3 or more fish. [

Geometric And Poisson Probability Distributions

Then :

Find the probability of catching 3 or more fish. [

POISSON distribution tables can be found in the tables tab main page

Geometric And Poisson Probability DistributionsEXAMPLE : Isabel Briggs Meyers developed personality type indicators. There are

16 personality types. One type that is “rare” is the INFJ ( introvert,

intuitive, feeling, judgmental) which occurs in 2.1% of the population.

Suppose a high school graduating class has 167 students, and a success

is the event that a student has the personality type INJF. a) Let be the number of successes ( INJF students ) in the

trials. If will the Poisson be a good approximation of the binomial ?

Geometric And Poisson Probability DistributionsEXAMPLE : Isabel Briggs Meyers developed personality type indicators. There are

16 personality types. One type that is “rare” is the INFJ ( introvert,

intuitive, feeling, judgmental) which occurs in 2.1% of the population.

Suppose a high school graduating class has 167 students, and a success

is the event that a student has the personality type INJF. a) Let be the number of successes ( INJF students ) in the

trials. If will the Poisson be a good approximation of the binomial ?

students

Geometric And Poisson Probability DistributionsEXAMPLE : Isabel Briggs Meyers developed personality type indicators. There are

16 personality types. One type that is “rare” is the INFJ ( introvert,

intuitive, feeling, judgmental) which occurs in 2.1% of the population.

Suppose a high school graduating class has 167 students, and a success

is the event that a student has the personality type INJF. a) Let be the number of successes ( INJF students ) in the

trials. If will the Poisson be a good approximation of the binomial ?

students- yes, this is a good approximation since there are

more than 100 students and our mean is less than 10

Geometric And Poisson Probability DistributionsEXAMPLE : Isabel Briggs Meyers developed personality type indicators. There are

16 personality types. One type that is “rare” is the INFJ ( introvert,

intuitive, feeling, judgmental) which occurs in 2.1% of the population.

Suppose a high school graduating class has 167 students, and a success

is the event that a student has the personality type INJF. a) Let be the number of successes ( INJF students ) in the

trials. If will the Poisson be a good approximation of the binomial ?

students- yes, this is a good approximation since there are more

than 100 students and our mean is less than 10

b) Estimate the probability that this class has 0, 1, 2, 3, or 4 people who

have the INJF personality type.

Geometric And Poisson Probability DistributionsEXAMPLE : Isabel Briggs Meyers developed personality type indicators. There are

16 personality types. One type that is “rare” is the INFJ ( introvert,

intuitive, feeling, judgmental) which occurs in 2.1% of the population.

Suppose a high school graduating class has 167 students, and a success

is the event that a student has the personality type INJF. a) Let be the number of successes ( INJF students ) in the

trials. If will the Poisson be a good approximation of the binomial ?

students- yes, this is a good approximation since there are more

than 100 students and our mean is less than 10

b) Estimate the probability that this class has 0, 1, 2, 3, or 4 people who

have the INJF personality type.Using the Poisson table and we see…

Geometric And Poisson Probability DistributionsEXAMPLE : Isabel Briggs Meyers developed personality type indicators. There are

16 personality types. One type that is “rare” is the INFJ ( introvert,

intuitive, feeling, judgmental) which occurs in 2.1% of the population.

Suppose a high school graduating class has 167 students, and a success

is the event that a student has the personality type INJF. a) Let be the number of successes ( INJF students ) in the

trials. If will the Poisson be a good approximation of the binomial ?

students- yes, this is a good approximation since there are more

than 100 students and our mean is less than 10

b) Estimate the probability that this class has 0, 1, 2, 3, or 4 people who

have the INJF personality type.Using the Poisson table and we see…

c) Find

Geometric And Poisson Probability DistributionsEXAMPLE : Isabel Briggs Meyers developed personality type indicators. There are

16 personality types. One type that is “rare” is the INFJ ( introvert,

intuitive, feeling, judgmental) which occurs in 2.1% of the population.

Suppose a high school graduating class has 167 students, and a success

is the event that a student has the personality type INJF. a) Let be the number of successes ( INJF students ) in the

trials. If will the Poisson be a good approximation of the binomial ?

students- yes, this is a good approximation since there are more

than 100 students and our mean is less than 10

b) Estimate the probability that this class has 0, 1, 2, 3, or 4 people who

have the INJF personality type.Using the Poisson table and we see…

c) Find