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X1, X2, .... Xn are independent observations on the random variable X with distribution function F(x). Then the distribution function of Y = Max (X1, X2, ..., Xn) is
- a)[F(x)]n
- b)1 - [F(x)]n
- c)1 - [1 - F(x)]n
- d)[1-F(x)]n
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
X1,X2, .... Xn are independent observations on the random variable X w...
[F(x)]n
Most Upvoted Answer
X1,X2, .... Xn are independent observations on the random variable X w...
Explanation:
Distribution function of Y:
- The random variable Y represents the maximum of n independent observations.
- The probability that Y is less than or equal to a particular value y is the same as the probability that each of the n observations is less than or equal to y.
- Since the observations are independent, the probability that all n observations are less than or equal to y is just the product of the individual probabilities.
- Therefore, the distribution function of Y is the nth power of the distribution function of X.
Answer:
- Therefore, the distribution function of Y = Max(X1, X2, ..., Xn) is [F(x)]n.
- This means that the probability that Y is less than or equal to a particular value y is equal to [F(y)]n, where F(y) is the distribution function of X.
Distribution function of Y:
- The random variable Y represents the maximum of n independent observations.
- The probability that Y is less than or equal to a particular value y is the same as the probability that each of the n observations is less than or equal to y.
- Since the observations are independent, the probability that all n observations are less than or equal to y is just the product of the individual probabilities.
- Therefore, the distribution function of Y is the nth power of the distribution function of X.
Answer:
- Therefore, the distribution function of Y = Max(X1, X2, ..., Xn) is [F(x)]n.
- This means that the probability that Y is less than or equal to a particular value y is equal to [F(y)]n, where F(y) is the distribution function of X.
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Community Answer
X1,X2, .... Xn are independent observations on the random variable X w...
Explanation:
Distribution function of Y:
- The distribution function of Y = Max(X1, X2, ..., Xn) is the probability that Y is less than or equal to a particular value y.
Probability that Y <=>
- The probability that Y is less than or equal to y is the probability that all of the observations X1, X2, ..., Xn are less than or equal to y.
- Since X1, X2, ..., Xn are independent observations, the probability that all of them are less than or equal to y is the product of their individual probabilities.
- Therefore, the distribution function of Y is [F(y)]n, where F(y) is the distribution function of X.
Final Answer:
- Therefore, the correct answer is option 'A': [F(y)]n.
Distribution function of Y:
- The distribution function of Y = Max(X1, X2, ..., Xn) is the probability that Y is less than or equal to a particular value y.
Probability that Y <=>
- The probability that Y is less than or equal to y is the probability that all of the observations X1, X2, ..., Xn are less than or equal to y.
- Since X1, X2, ..., Xn are independent observations, the probability that all of them are less than or equal to y is the product of their individual probabilities.
- Therefore, the distribution function of Y is [F(y)]n, where F(y) is the distribution function of X.
Final Answer:
- Therefore, the correct answer is option 'A': [F(y)]n.
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X1,X2, .... Xn are independent observations on the random variable X with distribution function F(x). Then the distribution function of Y = Max (X1, X2, ..., Xn) isa)[F(x)]nb)1 - [F(x)]nc)1 - [1 - F(x)]nd)[1-F(x)]nCorrect answer is option 'A'. Can you explain this answer?
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X1,X2, .... Xn are independent observations on the random variable X with distribution function F(x). Then the distribution function of Y = Max (X1, X2, ..., Xn) isa)[F(x)]nb)1 - [F(x)]nc)1 - [1 - F(x)]nd)[1-F(x)]nCorrect answer is option 'A'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about X1,X2, .... Xn are independent observations on the random variable X with distribution function F(x). Then the distribution function of Y = Max (X1, X2, ..., Xn) isa)[F(x)]nb)1 - [F(x)]nc)1 - [1 - F(x)]nd)[1-F(x)]nCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for X1,X2, .... Xn are independent observations on the random variable X with distribution function F(x). Then the distribution function of Y = Max (X1, X2, ..., Xn) isa)[F(x)]nb)1 - [F(x)]nc)1 - [1 - F(x)]nd)[1-F(x)]nCorrect answer is option 'A'. Can you explain this answer?.
X1,X2, .... Xn are independent observations on the random variable X with distribution function F(x). Then the distribution function of Y = Max (X1, X2, ..., Xn) isa)[F(x)]nb)1 - [F(x)]nc)1 - [1 - F(x)]nd)[1-F(x)]nCorrect answer is option 'A'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about X1,X2, .... Xn are independent observations on the random variable X with distribution function F(x). Then the distribution function of Y = Max (X1, X2, ..., Xn) isa)[F(x)]nb)1 - [F(x)]nc)1 - [1 - F(x)]nd)[1-F(x)]nCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for X1,X2, .... Xn are independent observations on the random variable X with distribution function F(x). Then the distribution function of Y = Max (X1, X2, ..., Xn) isa)[F(x)]nb)1 - [F(x)]nc)1 - [1 - F(x)]nd)[1-F(x)]nCorrect answer is option 'A'. Can you explain this answer?.
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