HEI - P N> 5 occurred what is the expected value of...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
University of Illinois Fall 2009 ECE 313: Hour Exam I Monday October 12, 2009 7:00 p.m. — 8:00 p.m. 100 Noyes Laboratory 1. [15 points] Let A , B , and C denote three events defined on a sample space Ω, and suppose that P ( A ) = 0 . 6 ,P ( B ) = P ( C ) = 0 . 3, and P ( B c C ) = P ( A B c C c ) = 0 . 2. (a) [5 points] Find P ( B C ). (b) [5 points] Find P ( B C c ). (c) [5 points] Find P (( A B C ) c ). 2. [10 points] A and B are events defined on a sample space Ω. Assume P ( A ) ,P ( B ) > 0. Mark each of the two statements below as TRUE or FALSE. No justification is needed. TRUE FALSE 2 2 If P ( A | B ) = P ( B | A ), then P ( A ) = P ( B ). 2 2 P ( A | B ) P ( B ) + P ( A c | B ) P ( B ) = P ( B ) . 3. [30 points] Especially in this problem, you must provide sufficient explanation to justify your numerical answers. A fair coin is tossed repeatedly until a Head occurs. N denotes the number of tosses. (a) [5 points] What is the expected value of N ? (b) [5 points] Find the numerical value of P { N > 5 } . (c) [10 points] Given that the event
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: P { N > 5 } occurred, what is the expected value of N ? (d) [10 points] Find the numerical value of E [cos( πN )]. 4. [20 points] A fair coin is tossed 10 times. Calculate the probability that the first 5 tosses are all Tails given that a total of 8 Tails occurred on the 10 tosses. 5. [25 points] Dilbert has 3 coins in his pocket, 2 of which are fair coins while the third is a biased coin with P ( H ) = p 6 = 1 2 . The probability that a coin chosen at random from his pocket will land Tails is 7 12 . (a) [10 points] What is the value of p ? (b) [15 points] Dilbert picks two coins at random from his pocket, tosses each coin once, and observes a Head and a Tail. What is the conditional probability that both coins are fair?...
View Full Document

This note was uploaded on 10/25/2010 for the course ECE 313 taught by Professor Milenkovic,o during the Spring '08 term at University of Illinois, Urbana Champaign.

Ask a homework question - tutors are online