Let F(x) = 2 p sin-1vx, for 0 (a) Check that F is a valid CDF, and ?nd the corresponding PDF f. (b) Explain how it is possible for f to be a valid PDF even though f(x) goes to 8 as x approaches 0 and...

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Let
F(x) = 2 p sin-1vx, for 0

(a) Check that F is a valid CDF, and ?nd the corresponding PDF f.

(b) Explain how it is possible for f to be a valid PDF even though f(x) goes to 8 as x approaches 0 and as x approaches 1.

Answered Same DayDec 26, 2021

Answer To: Let F(x) = 2 p sin-1vx, for 0 (a) Check that F is a valid CDF, and ?nd the corresponding PDF f. (b)...

Robert answered on Dec 26 2021

118 Votes

Ans. 1
To check for the validity of the distribution , the distribution function should follow the
conditions, ( ) 0 whenF x x  , ( ) 1, whenF x x  ,
Take the derivative of the given function for the calculation of CDF ,
1
'
2sin ( ) / 1
( ) ( )
(1 )
d x
f x F x
dx x x


...

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Let F(x) = 2 p sin-1vx, for 0 (a) Check that F is a valid CDF, and ?nd the corresponding PDF f. (b) Explain how it is possible for f to be a valid PDF even though f(x) goes to 8 as x approaches 0 and...

Answer To: Let F(x) = 2 p sin-1vx, for 0 (a) Check that F is a valid CDF, and ?nd the corresponding PDF f. (b)...

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