Probability and Statistics (Quartiles) Q: Find the upper and lower quartiles of the random variabl

iyiswad9k 2022-05-02 Answered
Probability and Statistics (Quartiles)
Q: Find the upper and lower quartiles of the random variable.
f ( x ) = 1 x ln ( 1.5 )
for 4 x 6
I set F ( x ) = 0.25 and F ( x ) = 0.75 to denote Q 1 and Q 3
This is what I got for the answers:
For
F ( X ) = 0.25 , x = 9.86
For
F ( X ) = 0.75 , x = 3.28
However, these answers are wrong as compared with my textbook. It should be:
For
F ( X ) = 0.25 , x = 4.43
For
F ( X ) = 0.75 , x = 5.42
Please help me. I don't know what I'm doing wrong.
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Answers (1)

Diya Bass
Answered 2022-05-03 Author has 20 answers
For x between 4 and 6 we have
F ( x ) = Pr ( X x ) = 4 x 1 ln ( 1.5 ) t d t = 1 ln ( 1.5 ) ( ln x ln 4 ) .
For the first quartile q 1 , we want
1 ln ( 1.5 ) ( ln ( q 1 ) ln 4 ) = 0.25.
To solve, note that the above equation is equivalent to
ln ( q 1 / 4 ) = ( 0.25 ) ln ( 1.5 ) .
Equivalently,
q 1 4 = exp ( ( 0.25 ) ln ( 1.5 ) ) = ( 1.5 ) 0.25 .
We get q 1 4.427. I am sure you can now take care of q 3
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