If Y is a continuous random variable and m is the median of the distribution, then m is such that P(Y ≤m) = P(Y ≥ m) = 1/2. If Y₁, Y₂,..., Y are independent, exponentially dis- tributed random variables with mean ß and median m, Example 6.17 implies that Y(n) max (Y₁, Y₂, ..., Yn) does not have an exponential distribution. Use the general form of Fy) (y) to show that P(Y(n) > m) = 1-(.5)".
If Y is a continuous random variable and m is the median of the distribution, then m is such that P(Y ≤m) = P(Y ≥ m) = 1/2. If Y₁, Y₂,..., Y are independent, exponentially dis- tributed random variables with mean ß and median m, Example 6.17 implies that Y(n) max (Y₁, Y₂, ..., Yn) does not have an exponential distribution. Use the general form of Fy) (y) to show that P(Y(n) > m) = 1-(.5)".
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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![6.82 If Y is a continuous random variable and m is the median of the distribution, then m is such
that P(Y ≤m) = P(Y ≥ m) = 1/2. If Y₁, Y₂, ..., Y, are independent, exponentially dis-
tributed random variables with mean ß and median m, Example 6.17 implies that Y(n) =
max (Y₁, Y₂, ..., Yn) does not have an exponential distribution. Use the general form of Fy) (y)
to show that P(Y(n) > m) = 1- (.5)".](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F763773a4-b59e-428b-8a3f-bc3dd5fb97d6%2F6fa3f472-dd92-4ec1-9b08-d24e4e769ec1%2F21xdrz_processed.png&w=3840&q=75)
Transcribed Image Text:6.82 If Y is a continuous random variable and m is the median of the distribution, then m is such
that P(Y ≤m) = P(Y ≥ m) = 1/2. If Y₁, Y₂, ..., Y, are independent, exponentially dis-
tributed random variables with mean ß and median m, Example 6.17 implies that Y(n) =
max (Y₁, Y₂, ..., Yn) does not have an exponential distribution. Use the general form of Fy) (y)
to show that P(Y(n) > m) = 1- (.5)".
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