(a) Calculate the median of X. (b) Note: No need to show the second derivative. Calculate the mode of X (you can take log of the PDF)

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Let X be a continuous random variable which has the following PDF,
1
f(x) =
-00 < x < o; 1 > 0 ; 0 e R
T 1? + (x – 0)2 '
(a)
Calculate the median of X.
(b)
Calculate the mode of X (you can take log of the PDF)
Note: No need to show the second derivative.
Transcribed Image Text:Let X be a continuous random variable which has the following PDF, 1 f(x) = -00 < x < o; 1 > 0 ; 0 e R T 1? + (x – 0)2 ' (a) Calculate the median of X. (b) Calculate the mode of X (you can take log of the PDF) Note: No need to show the second derivative.
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