HW03_2011 - X tends to be bigger than Y . 3.6. Suppose X =...

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

View Full Document Right Arrow Icon
PROF Y. HONG FALL 2011 ECONOMICS 6190 PROBLEM SET # 3 3.1 Can two independent events A and B be mutually exclusive? Can two mutually exclusive events A and B be independent? Give your reasoning. 3.2. Give an example to show that P ( A \ B \ C ) = P ( A ) P ( B ) P ( C ) cannot guarantee P ( A \ B ) = P ( A ) P ( B ) . 3.3. Seven balls are distributed randomly into seven cells. Let X i = the number of cells containing exactly i balls. What is the probability distribution of X 3 P ( X = x ) for every possible x .) 3.4. [C±B, # 1.47, p.43] Prove that the following functions are cumulative distribution func- tions(CDF²s): (1) 1 2 + 1 tan 1 ( x ) ; x 2 ( ; + 1 ); (2) (1 + e x ) 1 ; x 2 ( ; + 1 ); (3) e e x ; x 2 ( ; + 1 ); (4) 1 e x ; x 2 (0 ; + 1 ) : 0 ; x ± 0 3.5. A CDF F X is stochastically greater than a CDF F Y if F X ( t ) ± F Y ( t ) for all t and F X ( t ) < F Y ( t ) for some t . Prove that if X ² F X and Y ² F Y , then P ( X > t ) ³ P ( Y > t ) for every t P ( X > t ) > P ( Y > t ) for some t; that is,
Background image of page 1

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

View Full DocumentRight Arrow Icon
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: X tends to be bigger than Y . 3.6. Suppose X = X 1 with probability p and X = X 2 with probability 1 &amp; p; where p 2 (0 ; 1) ; X 1 and X 2 are random variables with CDFs F 1 ( x ) and F 2 ( x ) respectively. Find the CDF of X: 1 3.7. An investment &amp;rm o/ers its customers municipal bonds that mature after varying numbers of years. Given that the cumulative distribution of T; the number of years to maturity for a randomly selected bond is F ( t ) = 8 &gt; &gt; &gt; &gt; &gt; &gt; &lt; &gt; &gt; &gt; &gt; &gt; &gt; : t &lt; 1 ; 1 4 1 &amp; t &lt; 3 ; 1 2 3 &amp; t &lt; 5 ; 3 4 5 &amp; t &lt; 7 ; 1 t 7 : Find (1) P ( T = 5); (2) P ( T &gt; 3); and (3) P (1 : 4 &lt; T &lt; 6) : Give your reasoning. 2...
View Full Document

This note was uploaded on 01/07/2012 for the course ECON 6190 taught by Professor Hong during the Fall '07 term at Cornell University (Engineering School).

Page1 / 2

HW03_2011 - X tends to be bigger than Y . 3.6. Suppose X =...

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

View Full Document Right Arrow Icon
Ask a homework question - tutors are online