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3. (Discrete distributions, From a recent statistical analysis for the last five years, on an average there are 3 (major) air accidents per month in the world. Let X be the number of air accidents occurred in a randomly selected month. It is known that X-Poisson(2) approximately, where the intensity λ = 3 accidents (average number of accidents per month). Find the probability that there will be 3 or more air accidents (1) in a given month of the next year; Hint: The required probability is P(X ≥ 3) where X~ Poisson(3). I (2) in 4 of the first 6 months of the next year; Hint: 4th 5th 6th || 1-p_1-p 6C4 different ways to specify 4 months рр р Р Define Y = # of months in the first 6 months of the next year in which "4 or more air accidents occur in a month". Y is a binomial distribution with n=6and p is the result from (1). Compute P(Y=4). Notice that for a given month, either "3 or more accidents will happen in the month (Success)" or "2 or less accidents will happen in the month (Failure)". |×|×|×|× | (3) for the first time in the next year in June; Hint: Define Y = # of months required to observe the first occurrence of the event (i.e., 3 or more air accidents occur in a month) (start from first month of next year). Notice that if the first occurrence is in June, the event did not happen from January to May. In other words, the event in this problem is (X<3, X<3, X<3, X<3, X<3, X23).

3. (Discrete distributions, From a recent statistical analysis for the last five years, on an average there are 3 (major) air accidents per month in the world. Let X be the number of air accidents occurred in a randomly selected month. It is known that X-Poisson(2) approximately, where the intensity λ = 3 accidents (average number of accidents per month). Find the probability that there will be 3 or more air accidents (1) in a given month of the next year; Hint: The required probability is P(X ≥ 3) where X~ Poisson(3). I (2) in 4 of the first 6 months of the next year; Hint: 4th 5th 6th || 1-p_1-p 6C4 different ways to specify 4 months рр р Р Define Y = # of months in the first 6 months of the next year in which "4 or more air accidents occur in a month". Y is a binomial distribution with n=6and p is the result from (1). Compute P(Y=4). Notice that for a given month, either "3 or more accidents will happen in the month (Success)" or "2 or less accidents will happen in the month (Failure)". |×|×|×|× | (3) for the first time in the next year in June; Hint: Define Y = # of months required to observe the first occurrence of the event (i.e., 3 or more air accidents occur in a month) (start from first month of next year). Notice that if the first occurrence is in June, the event did not happen from January to May. In other words, the event in this problem is (X<3, X<3, X<3, X<3, X<3, X23).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
Problem 27T
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From a recent stätistical analysis for the last five years, on an 3. (Discrete distributions, average there are 3 (major) air accidents per month in the world. Let X be the number of air accidents occurred in a randomly selected month. It is known that X~ Poisson(A) approximately, where the intensity 2 = 3 accidents (average number of accidents per month). Find the probability that there will be 3 or more air accidents (1) in a given month of the next year; Hint: The required probability is P(X > 3) where X ~ Poisson(3). (2) in 4 of the first 6 months of the next year; Hint: 1st 4th 5th 6th | × | × | × | × | | | P p p p C4 different ways to specify 4 months 1-р 1-р Define Y = # of months in the first 6 months of the next year in which “4 or more air accidents occur in a month". Y is a binomial distribution with n=6and p is the result from (1). Compute %3D P(Y = 4). Notice that for a given month, either "3 or more accidents will happen in the month (Success)" or "2 or less accidents will happen in the month (Failure)". (3) for the first time in the next year in June; Hint: Define Y = # of months required to observe the first occurrence of the event (i.e., 3 or more air accidents occur in a month) (start from first month of next year). Notice that if the first occurrence is in June, the event did not happen from January to May. In other words, the event in this problem is (X<3, X<3, X<3, X<3, X<3, X23).
Transcribed Image Text:From a recent stätistical analysis for the last five years, on an 3. (Discrete distributions, average there are 3 (major) air accidents per month in the world. Let X be the number of air accidents occurred in a randomly selected month. It is known that X~ Poisson(A) approximately, where the intensity 2 = 3 accidents (average number of accidents per month). Find the probability that there will be 3 or more air accidents (1) in a given month of the next year; Hint: The required probability is P(X > 3) where X ~ Poisson(3). (2) in 4 of the first 6 months of the next year; Hint: 1st 4th 5th 6th | × | × | × | × | | | P p p p C4 different ways to specify 4 months 1-р 1-р Define Y = # of months in the first 6 months of the next year in which “4 or more air accidents occur in a month". Y is a binomial distribution with n=6and p is the result from (1). Compute %3D P(Y = 4). Notice that for a given month, either "3 or more accidents will happen in the month (Success)" or "2 or less accidents will happen in the month (Failure)". (3) for the first time in the next year in June; Hint: Define Y = # of months required to observe the first occurrence of the event (i.e., 3 or more air accidents occur in a month) (start from first month of next year). Notice that if the first occurrence is in June, the event did not happen from January to May. In other words, the event in this problem is (X<3, X<3, X<3, X<3, X<3, X23).
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