{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

20082ee131A_1_HW4SOL

# 20082ee131A_1_HW4SOL - EE 131A Homework#4 Solution Spring...

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

EE 131A Homework #4 Solution Spring 2008 K. Yao 1. We know A B = φ. (a) If A and B are independent, Pr ( A ) Pr ( B ) = Pr ( A B ) = 0 because A B = φ. Therefore Pr ( A ) = 0 or Pr ( B ) = 0 or both equal 0 . . (b) If Pr ( A ) = 0 or Pr ( B ) = 0 or both equal to 0, we have Pr ( A ) Pr ( B ) = 0 . But Pr ( A B ) = 0 because A B = φ. Therefore Pr ( A B ) = Pr ( A ) Pr ( B ) and A and B are independent. 2. Let hypothesis H k denote that a coin of type k was drawn. Its prior probability is 1 9 . Bayes rule tells us that the posterior probability of hypothesis H k is Pr ( H k | 7 H out of 25) = C 25 7 π 7 k (1 - π k ) 18 9 m =1 C 25 7 π 7 m (1 - π m ) 18 . Since the denominator in the above expression does not dependent on k, we only need to consider the maximiation of p m (1 - p ) n - m with respect to p where p = m/n. In our case, we know maximization occurs at m/n = 7 / 25 = 0 . 28 . This shows we should decide on H 3 or coin type 3 since π 3 = 0 . 3 . 3. X is a random variable with a binomial distribution with parameter n and p = 0 . 9 a. Prob. the system will declare an airplane = P (1 X 2) = 1 - P ( X = 0) = 1 - 2 0 (0 . 9) 0

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 ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern