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Math Help - Bernoulli vs binomial vs Poisson models?

  1. #1
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    Bernoulli vs binomial vs Poisson models?

    I'm a little confused about the difference between the Bernoulli and binomial? Is the Bernoulli model just one trial of a binomial model? Poisson I know is the model to use when one measures rare events over a period of time.

    Which is the appropriate statistical model for the situations below? Any of the above three or none of them?

    1. You roll 12 dice. You win if at least 6 dice come up with 6's.
    Confused...could this be poisson since it measures whether or not 6's are rolled?

    2. We record hair color found in a group of 100 people.
    This is not Bernoulli, binomial, or Poisson, right?

    3. A computer monitor manufacturing plant chooses one monitor per hour for quality inspection. One measurement is the number of scratches greater than 3 mm on the back surface.
    Bernoulli, since it's only 1 monitor per hour and the machine either has the defect or it doesn't? Is that right?

    4. An aquarium has 14 red guppies and 12 yellow guppies. Six guppies are netted out at random. Measure the number of yellow guppies netted out.
    Bernoulli or binomial? Each trial would be bernoulli but the whole thing would be binomial right since it's more than one trial?

    5. A study found that 60% of all high school students have plagiarized at one point or another. A teacher conducts a survey at his school and found that 212 students out of 455 have plagiarized.
    Binomial, since the students have either plagiarized or haven't? Right?

    6. You're trying to estimate the toxicity of DDT on lake trout. You test 15 concentration levels: 5 ppm, 15 ppm, 25 ppm, etc. up to 1000 ppm. Each level is tested on one trout. Y is the total number of trout out of 10 that die.
    Poisson? Number of trout that die. But could it be a bernoulli trial because either the trout die or don't?

    7. You're bowling at a bowling alley. You keep playing until you get a strike. X is the total number of attempts you make.
    This is Poisson I think. It measures the number of a certain event in a number of tries. Or is it binomial, since you either get a strike or you don't?

    I'm really confused about distinguishing between the three. I think explaining the above situations would be really helpful. Thanks.
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  2. #2
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    Quote Originally Posted by virtuoso735 View Post
    I'm a little confused about the difference between the Bernoulli and binomial? Is the Bernoulli model just one trial of a binomial model? Poisson I know is the model to use when one measures rare events over a period of time.

    Which is the appropriate statistical model for the situations below? Any of the above three or none of them?

    1. You roll 12 dice. You win if at least 6 dice come up with 6's.
    Confused...could this be poisson since it measures whether or not 6's are rolled?

    2. We record hair color found in a group of 100 people.
    This is not Bernoulli, binomial, or Poisson, right?

    3. A computer monitor manufacturing plant chooses one monitor per hour for quality inspection. One measurement is the number of scratches greater than 3 mm on the back surface.
    Bernoulli, since it's only 1 monitor per hour and the machine either has the defect or it doesn't? Is that right?

    4. An aquarium has 14 red guppies and 12 yellow guppies. Six guppies are netted out at random. Measure the number of yellow guppies netted out.
    Bernoulli or binomial? Each trial would be bernoulli but the whole thing would be binomial right since it's more than one trial?

    5. A study found that 60% of all high school students have plagiarized at one point or another. A teacher conducts a survey at his school and found that 212 students out of 455 have plagiarized.
    Binomial, since the students have either plagiarized or haven't? Right?

    6. You're trying to estimate the toxicity of DDT on lake trout. You test 15 concentration levels: 5 ppm, 15 ppm, 25 ppm, etc. up to 1000 ppm. Each level is tested on one trout. Y is the total number of trout out of 10 that die.
    Poisson? Number of trout that die. But could it be a bernoulli trial because either the trout die or don't?

    7. You're bowling at a bowling alley. You keep playing until you get a strike. X is the total number of attempts you make.
    This is Poisson I think. It measures the number of a certain event in a number of tries. Or is it binomial, since you either get a strike or you don't?

    I'm really confused about distinguishing between the three. I think explaining the above situations would be really helpful. Thanks.
    1. X ~ Binomial(n = 12, p = 1/6).

    2. Right.

    3. Is the random variable number of scratches greater then 3mm on the back of a computer monitor?

    4. The number of yellow fish follows a Hypergeometric distribution.

    5. X ~ Binomial(n = 455, p = 0.6).

    6. Not sure at the moment.

    7. Number of attempts until a strike follows a geometric distribution.
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  3. #3
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    Thanks for your reply. How is the geometric related to the Bernoulli or Bionomial distributions? They're not the same right?

    #3 - Yes, it's the number of scratches greater than 3 mm.
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