Post on 17-Jan-2018
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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