# ) From a recent statistical

SoccerBoss
Category:
Statistics
Price: \$15 USD

Question description

) From a recent statistical analysis for the last five years, on an average there

are 4 (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(l) approximately, where the intensity

l» 4 accidents (monthly average number of accidents). Find the probability that there will be 4 or

more air accidents

(1) in a given month of the next year;  Hint: The required probability is P(X ³ 4).

Ans.

(2) in 4 of the first 6 months of the next year;

Hint:  1st  4th  5th  6th

|  ×  |  ×  |  ×  |  ×  |  |  |  6C4 different ways to specify 4 months

p  p  p  p  1-p  1-p

Event

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 has a binomial distribution. Compute P(Y = 4).

Ans.

(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 A (i.e., 4 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<4, X<4, X<4, X<4, X<4, X≥4).

Ans.

(4) Compare the probabilities calculated in (2) and (3), and why explain these probabilities are larger or smaller.

Ans.

(Top Tutor) Daniel C.
(997)
School: New York University
Studypool has helped 1,244,100 students

1831 tutors are online

Brown University

1271 Tutors

California Institute of Technology

2131 Tutors

Carnegie Mellon University

982 Tutors

Columbia University

1256 Tutors

Dartmouth University

2113 Tutors

Emory University

2279 Tutors

Harvard University

599 Tutors

Massachusetts Institute of Technology

2319 Tutors

New York University

1645 Tutors

Notre Dam University

1911 Tutors

Oklahoma University

2122 Tutors

Pennsylvania State University

932 Tutors

Princeton University

1211 Tutors

Stanford University

983 Tutors

University of California

1282 Tutors

Oxford University

123 Tutors

Yale University

2325 Tutors