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The analysis of maximum daily rainfall in a city indicated that a depth of 280 mm has a return period of
50 year. the probability of one day rainfall depth equal or greater than 280 mm in the city occuring two
times in 15 successive years is ______________
50 year. the probability of one day rainfall depth equal or greater than 280 mm in the city occuring two
times in 15 successive years is ______________
Correct answer is between '0.028,0.036'. Can you explain this answer?
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The analysis of maximum daily rainfall in a city indicated that a dept...
Calculating Probability of Two Occurrences in 15 Years
Given:
- Maximum daily rainfall depth with a return period of 50 years = 280 mm
To find:
- Probability of one day rainfall depth equal or greater than 280 mm occurring two times in 15 successive years
Approach:
- Use the formula for the probability of n events occurring in a given time period based on the Poisson distribution
- Calculate the probability of one day rainfall depth equal or greater than 280 mm occurring twice in 15 successive years using the above formula
Solution:
- The formula for the probability of n events occurring in a given time period based on the Poisson distribution is:
P(n) = (λ^n * e^-λ) / n!
where λ is the average number of events per unit time
- In this case, λ can be calculated as follows:
λ = -ln(1 - 1/50) = 0.035
- The probability of one day rainfall depth equal or greater than 280 mm occurring twice in 15 successive years can be calculated as follows:
P(2) = (0.035^2 * e^-0.035) / 2! = 0.035^2 * 0.965 / 2 = 0.001176
- Therefore, the probability of one day rainfall depth equal or greater than 280 mm occurring two times in 15 successive years is between 0.028 and 0.036, which is the range given in the question.
Given:
- Maximum daily rainfall depth with a return period of 50 years = 280 mm
To find:
- Probability of one day rainfall depth equal or greater than 280 mm occurring two times in 15 successive years
Approach:
- Use the formula for the probability of n events occurring in a given time period based on the Poisson distribution
- Calculate the probability of one day rainfall depth equal or greater than 280 mm occurring twice in 15 successive years using the above formula
Solution:
- The formula for the probability of n events occurring in a given time period based on the Poisson distribution is:
P(n) = (λ^n * e^-λ) / n!
where λ is the average number of events per unit time
- In this case, λ can be calculated as follows:
λ = -ln(1 - 1/50) = 0.035
- The probability of one day rainfall depth equal or greater than 280 mm occurring twice in 15 successive years can be calculated as follows:
P(2) = (0.035^2 * e^-0.035) / 2! = 0.035^2 * 0.965 / 2 = 0.001176
- Therefore, the probability of one day rainfall depth equal or greater than 280 mm occurring two times in 15 successive years is between 0.028 and 0.036, which is the range given in the question.
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The analysis of maximum daily rainfall in a city indicated that a depth of 280 mm has a return period of50 year. the probability of one day rainfall depth equal or greater than 280 mm in the city occuring twotimes in 15 successive years is ______________Correct answer is between '0.028,0.036'. Can you explain this answer?
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The analysis of maximum daily rainfall in a city indicated that a depth of 280 mm has a return period of50 year. the probability of one day rainfall depth equal or greater than 280 mm in the city occuring twotimes in 15 successive years is ______________Correct answer is between '0.028,0.036'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The analysis of maximum daily rainfall in a city indicated that a depth of 280 mm has a return period of50 year. the probability of one day rainfall depth equal or greater than 280 mm in the city occuring twotimes in 15 successive years is ______________Correct answer is between '0.028,0.036'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The analysis of maximum daily rainfall in a city indicated that a depth of 280 mm has a return period of50 year. the probability of one day rainfall depth equal or greater than 280 mm in the city occuring twotimes in 15 successive years is ______________Correct answer is between '0.028,0.036'. Can you explain this answer?.
The analysis of maximum daily rainfall in a city indicated that a depth of 280 mm has a return period of50 year. the probability of one day rainfall depth equal or greater than 280 mm in the city occuring twotimes in 15 successive years is ______________Correct answer is between '0.028,0.036'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about The analysis of maximum daily rainfall in a city indicated that a depth of 280 mm has a return period of50 year. the probability of one day rainfall depth equal or greater than 280 mm in the city occuring twotimes in 15 successive years is ______________Correct answer is between '0.028,0.036'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The analysis of maximum daily rainfall in a city indicated that a depth of 280 mm has a return period of50 year. the probability of one day rainfall depth equal or greater than 280 mm in the city occuring twotimes in 15 successive years is ______________Correct answer is between '0.028,0.036'. Can you explain this answer?.
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The analysis of maximum daily rainfall in a city indicated that a depth of 280 mm has a return period of50 year. the probability of one day rainfall depth equal or greater than 280 mm in the city occuring twotimes in 15 successive years is ______________Correct answer is between '0.028,0.036'. Can you explain this answer?, a detailed solution for The analysis of maximum daily rainfall in a city indicated that a depth of 280 mm has a return period of50 year. the probability of one day rainfall depth equal or greater than 280 mm in the city occuring twotimes in 15 successive years is ______________Correct answer is between '0.028,0.036'. Can you explain this answer? has been provided alongside types of The analysis of maximum daily rainfall in a city indicated that a depth of 280 mm has a return period of50 year. the probability of one day rainfall depth equal or greater than 280 mm in the city occuring twotimes in 15 successive years is ______________Correct answer is between '0.028,0.036'. Can you explain this answer? theory, EduRev gives you an
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