{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

hw1-sol

hw1-sol - AMS 311(Fall 2009 Joe Mitchell Homework Set 1...

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

View Full Document Right Arrow Icon
AMS 311 (Fall, 2009) Joe Mitchell Homework Set # 1 – Solution Notes (1). (13 points) Problem 5, Ross, Chapter 2. (same problem in 7th or 8th edition) (a). Since each x i is either 0 or 1 (2 choices), the total number of choices for the outcome vector, ( x 1 ,x 2 ,x 3 ,x 4 ,x 5 ), is 2 5 .Thu s , | S | =2 5 = 32. (b). W has 15 elements, namely: W = { (1,1,0,0,0), (1,1,0,0,1), (1,1,0,1,0), (1,1,0,1,1), (1,1,1,0,0), (1,1,1,0,1), (1,1,1,1,0), (1,1,1,1,1), (0,0,1,1,0), (0,0,1,1,1), (0,1,1,1,0), (0,1,1,1,1), (1,0,1,1,0), (1,0,1,1,1), (1,0,1,0,1) } . (c). Since A consists of outcomes having x 4 = x 5 = 0, we see that there are 2 choices for each of x 1 ,x 2 ,x 3 ;thus , A has 2 · 2 · 2 = 8 elements. (You should be able to list them.) (d). A W = { (1 , 1 , 0 , 0 , 0) , (1 , 1 , 1 , 0 , 0) } , since these are the only two elements of W having x 4 = x 5 = 0. (2). (16 points) Among 33 students in a class, 17 of them earned A’s on the midterm exam, 14 earned A’s on the Fnal exam, and 11 did not earn A’s on either examination. What is the probability that a randomly selected student from this class earned an A on both exams? What is the sample space and event, in your notation? The “experiment” is the selection of one student from the class of 33; we can record the “out- come” as a pair ( m,f ), where m is the grade the student made on the midterm and f is the grade the student made on the ±nal. The sample space is the set S of 33 students. Let E be the event that the selected student makes an “A” on the midterm; we know that P ( E ) = 17 / 33. Let F be the event that the student earns an “A” on the ±nal; we know that P ( F ) = 14 / 33. We are also told that P ( E c F c ) = 11 / 33 = 1
Background image of page 1

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

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 3

hw1-sol - AMS 311(Fall 2009 Joe Mitchell Homework Set 1...

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

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