Let Y_(1),Y_(2),...,Y_(n) be independent, uniformly distributed random variables on the interval [0, theta]. density function of Y_(n)

memLosycecyjz

memLosycecyjz

Answered question

2022-09-25

Let Y 1 , Y 2 , . . . , Y n be independent, uniformly distributed random variables on the interval [ 0 , θ ]. density function of Y ( n )

Answer & Explanation

Cremolinoer

Cremolinoer

Beginner2022-09-26Added 11 answers

Density function of maximum:
g ( n ) ( y ) = n [ F ( y ) ] n 1 f ( y )
Density function of minimum:
g ( 1 ) ( y ) = n [ 1 F ( y ) ] n 1 f ( y )
Y i are uniformly distributed on [ 0 , θ ] :
F ( y ) = y 0 θ 0 = y θ if 0 y θ
f ( y ) = 1 θ 0 = 1 θ if 0 y θ
We need to determine the probability density function of the maximum:
g ( n ) ( y ) = n [ F ( y ) ] n 1 f ( y ) = n ( y θ ) n 1 1 θ = n y n 1 θ n
Result:
g ( n ) ( y ) = n y n 1 θ n

Do you have a similar question?

Recalculate according to your conditions!

New Questions in College Statistics

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?