hw8_418_10

# hw8_418_10 - 1 1 a 1 c(1 x2)dx = 1 then c = 3 4 x x b F(x =...

This preview shows pages 1–2. Sign up to view the full content.

1. a) 1 - 1 c (1 - x 2 ) dx = 1, then c = 3 4 . b) F ( x ) = x -∞ f ( t ) dt = x - 1 3 4 (1 - t 2 ) dt = - 1 / 4 x 3 + 3 / 4 x + 1 / 2 , F ( x ) = 0 if x ≤ - 1; - 1 / 4 x 3 + 3 / 4 x + 1 / 2 if - 1 < x < 1; 1 if x 1 . 3. For f to be a valid pdf, it must satisfy 2 conditions:1) f ( x ) 0 , for any x; 2) -∞ = 1. a) f (1) = c,f (2) = - 4 c . So, there is no c that makes f (1) and f (2) be positive at the same time. So, f cannot be a pdf. b) f (1 / 2) = 3 c 4 ,f (7 / 3) = - 7 c 9 , but there is no c that makes f (1 / 2) and f (7 / 3) be positive at the same time. So, f cannot be a pdf. 4. a) p ( x > 20) = 20 10 x 2 dx = 1 / 2 b) F ( x ) = x 10 10 t 2 dt = 1 - 10 /x , hence F ( x ) = { 0 if x 10; 1 - 10 /x if x > 1 . c) p ( x 15) = 1 - p ( x 15) = 1 - (1 - 10 / 15) = 2 / 3 . Let X denotes the lifetime of a certain type of electronic device, then X B (6 , 2 / 3), then 1 - p ( X 2) = 1 - (0 . 00137 + 0 . 1646 + 0 . 0823) = 0 . 899. 5.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

hw8_418_10 - 1 1 a 1 c(1 x2)dx = 1 then c = 3 4 x x b F(x =...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online