Question

Statistical Model for these?

1. For each random variable described below, decide whether the appropriate statistical model is Binomial, Poisson, Bernoulli, or none of these. Give some reason for your decision.

a. You take a test with 15 questions. Each is right or wrong. X is the number of questions you answer correctly.

b. X is the number of eggs laid by a lionfish (mean 30,000, BTW, and they can lay eggs up to every four days)

c. You play the lottery once per week. X is the number of times you play until you win a prize of at least $100.

d. An urn contains 20 red balls and 30 white balls. You draw out 10 balls at random without replacement. X is the number of red balls in your sample.

e. X is the number of times you die each day.

f. A poll is taken of 1000 random Americans. X is the number of people who think Global warming is really happening.

g. X is the number of flying-bomb hits in the south of London during one raid during World War II.

Thank you for your help!!

Answer 1

a)

Here we have 15 independent questions, that is we have 15 independent trials.

Each of the trial has two outcomes: right or wrong

Here X has binomial distribution with parameters n=15 and p = 0.50.

b)

Here X has Poisson distribution with parameter .

c)

Here X has geometric distribution. It is not Binomial, Poisson, or Bernoulli.

Answer: none of these

d)

Since draws are without replacement so it is not binomial.

Here X has hypergeometric distribution.

Answer: none of these