{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

hw4 - Stats 116 HW5 August 2 2007 16(a A happens iff at...

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

View Full Document Right Arrow Icon

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

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

Unformatted text preview: Stats 116: HW5 August 2, 2007 16. (a) A happens iff at least one A i happens, so that A = ∪ n i =1 A i . (b) if A i happens, it means all points P j for j negationslash = i are to the left of P i going clockwise, or A i is to the right of P j , which contradict A j , i.e A i and A j are mutually exclusive. (c) Since the A i are mutually exclusive, P( A ) = n summationdisplay i =1 P( A i ) = n P( A 1 ) the last equality is by symmetry. Given P 1 , each other point has probability one half to fall in the left semi-circle, so that P( A 1 ) = 1 2 n- 1 , and P( A ) = n 1 2 n- 1 20. (a) f ( x, y ) = g ( x ) h ( y ), with g ( x ) = xe- x , and h ( y ) = e- y , which both are proper densities, hence X and Y are independent. (b) P( Y ≤ . 5) > 0 and P( X > . 5) > 0, but P( X > . 5 , Y ≤ . 5) = 0 since X < Y . Then P( X > . 5 , Y ≤ . 5) negationslash = P( Y ≤ . 5)P( X > . 5) and X and Y are not independent 26. (a) Since A , B and C are independent, the joint cdf is just the product of the marginal cdfs...
View Full Document

{[ snackBarMessage ]}