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351 SMAM Name_______________
Quiz 2 N Solution
1. The probability that an integrated circuit chip will have defective etching is 0.12, the probability that it will have a crack defect is 0.29 and the probability that it has both defects is 0.07. What is the probability that an integrated circuit chip has A. at least one of the two kinds of defects? (4 points) Let A be event of defective etching, B be the event of a crack defect, P(A) = 0.12 P(B) = 0.29 P(A B) = 0.07 P(A B) = P(A) + P(B) P(A B) = 0.12+0.29 0.07 = .34 B. neither defect? (4 points) P(A B ) = P(A = B) 1P(A B) = 1 .34 = .66
C. a crack defect but does not have defective etching? (4 points) P(B A) = P(B) P(B A) = 0.29 0.07 = 0.22 2. How many code words may be formed using the letter A twice, the letter B three times and the letter C four times? (4 points)
9! = 1260 2!3!4! 3. A car rental agency has 18 compact cars and 12 intermedia...

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RIT - SMAM - 351

SMAM 351Quiz 3 d SolutionName_1.A family has three telephone lines one for general use, one for internet access and a teen line. The probability distribution of the number of lines Y in use is given in the table below. Y 0 1 2 3 p(y) 0.2 0.3 0.

RIT - SMAM - 351

SMAM 351Quiz 4 NName_1. The thickness of wood paneling (in inches) that a customer orders is a random variable X with probability mass function x 0.125 0.250 0.375 f(x) 0.2 0.7 0.1 A. Find the mean and the standard deviation of X. (8 points) =

RIT - SMAM - 351

SMAM 351Quiz 5dName_1. The weight distribution of parcels sent in a certain manner is a normally distributed random variable X with mean 10 lb. and standard deviation 2 lbs. Find: A. P(6 X 14) (5 points) 14 10 6 10 P(6 X 14) = P <Z < 2

RIT - SMAM - 351

SMAM 351Quiz 5nName_1. Suppose that the force acting on a column that helps support a building is normally distributed with mean 15.0 kips and standard deviation 1.25 kips. A. What is the probability that the force is at most 17 kips? 17 15 P

RIT - SMAM - 351

SMAM 351Quiz 6 dName_The following formulae will prove helpful. 1 x F(x;,) = 0 x <0 f(x;,) = x 1e x 0 () = 1-e -(x/ ) x 0 0 otherwise () = ( 1)( 1) 1 ( x ) x e f(x;,) = 0 x0 x<0 1 = 1+ 1 = 21. The life in years of a certai

RIT - SMAM - 351

SMAM 351Quiz 6 nName_The following formulae will prove helpful. 1 x F(x;,) = 0 x <0 f(x;,) = x 1e x 0 () = 1-e -(x/ ) x 0 0 otherwise () = ( 1)( 1) 1 ( x ) x e f(x;,) = 0 x0 x<0 1 = 1+ 1 = 21. Statistics released by the Na

RIT - SMAM - 351

INFORMATION ABOUT SMAM 351 Course Title: Probability and Statistics Textbook: PROBABILITY AND STATISTICS FOR ENGINEERING AND THE SCIENCES Sixth Edition by Jay L. Devore Duxbury Press Course Content: An introduction to basic concepts of Probability an

RIT - SMAM - 351

Computer Assignment 1 due 4/20/061.Use Minitab to do this problem. The probability that a car stolen in a certain western city will be recovered is 0.65. Out of 40 cars what is the probability A. At least 25 are recovered? MTB > cdf 24 c1; SUBC> bi

RIT - SMAM - 351

SMAM 351Quiz 1Name_Suppose that vehicles taking a particular freeway can turn right (R), turn left (L), or go straight (S). Consider observing the direction for each of three sucessive vehicles. A. List all the outcomes in the event C that exac

RIT - SMAM - 351

SMAM 351Homework Quiz 2Name_Let A denote the event that the next request for assistance from a statistical software consultant relates to the SPSS package, and let B be the event that the next request is for help with SAS. Suppose that P(A)=.30

RIT - SMAM - 351

SMAM 351Quiz 4Name_You may use your book for tables only. 1.Supppose that 25% of all drivers come to a complete stop at an intersection having flashing red lights in all directions when no other cars are visible. What is the probability that of

RIT - SMAM - 351

SMAM 351Quiz 5Name_1. Suppose that the force acting on a column that helps to support a building is normally distributed with mean 15.0 kips and standard deviation 1.25 kips. What is the probability that the force is between 10 and 12 kips?12

RIT - SMAM - 351

SMAM 351Quiz6Name_1. Use the normal approximation to the binomial distribution with the continuity correction to do this problem. Suppose only 40% of the drivers in a certain state regularly wear a seat belt. A random sample of 500 drivers is s

RIT - SMAM - 351

SMAM 351Quiz 7Name_1. The continuous joint density function of the random variables X and Y is 6x, f ( x , y= ) 0 0 < x < 1,0 < y < 1 x elsewhereFind E(XY) by setting up and calculating an appropriate double integral.EXY = 1 1 x 0 0

RIT - SMAM - 351

SMAM 351Assignments Spring 2004Dr. Gruber SectionsChapter 2 2.1: 57: 2, 3,4, 5, 8 2.2: 64: 11,12,13, 14,15, 17,18, 19,20,21,22, 25 2.3: 73: 29,30,32,33,36,37,42, 43 2.4 :83: 45, 47, 50, 53, 55 ,57,58 59,60,61, 62, 65 2.5: 90: 69, 73, 74, 75, 7

RIT - SMAM - 351

SMAM 351Exam 1nNAME_1. A factory operates three different shifts. During a year period there were 200 accidents. Some of the accidents were attributed to unsafe working conditions . The other accidents were not related to working conditions. Th

RIT - SMAM - 351

SMAM 351Exam 4d Name_1. The time to failure of an electronic component has an exponential distribution with probability density function f(x) = .001e .001x,x > 0A. What is the probability the component lasts at most 1200 hours?(8 points) P(X 1

RIT - SMAM - 351

SMAM 351Exam 4n Name_1. The time to failure of an electronic component has an exponential distribution with probability density function f(x) = .001e .001x,x > 0A. What is the probability the component lasts at most 1500 hours?(8 points) P(X 1

RIT - SMAM - 351

#2 Due12/13/04 1. A lot contains 20 items. A. How many different samples of size 4 may be selected if (1) sampling is without replacement? 20 = 4845 4(2) sampling is with replacement? 204 = 160000 B. Suppose that the lot contains three defective

RIT - SMAM - 351

#5 Due 4/9/04 1. A process for making plate glass produces an average of four seeds(small bubbles) per 100 square feet. Using the Poisson distribution find the probability that A. a particular piece of glass 10 ft by 10 ft will contain exactly three

RIT - SMAM - 351

SMAM 351 Homework #7 Due 4/23/04 1.The life of a certain type of small motor is normally distributed with mean 10 years and standard deviation 1.5 years. The manufacturer will replace for free all motors that fail while under guarantee. He is only wi

RIT - SMAM - 351

SMAM 351 Makup Exam 4 Day Name_ Rules 1. DO YOUR OWN WORK. DO NOT CONSULT ANYBODY ALIVE OR DEAD. 2. Exam may be done by anyone whose grade in class was less than 80%. It is highly recommended for students who scored below 70%. 3. Show your work in th

RIT - SMAM - 351

SMAM 351 1. GivenReview for Exam 3f(x) = k(1+ 2x),0 < x < 2 Find A. k so that f is a pdf B. The mean and the variance of f(x) C. The cumulative distribution function D. The median of f(x) E. Compare the exact value of P(X |< 1.25] to the lower b

RIT - SMAM - 351

SMAM 351Worksheet 21.A company subjects prospective employees to two drug tests with independent outcomes. Both tests are 98% accurate in determining whether someone is using drugs. What is the probability that A. A nonuser fails both testsB A

RIT - SMAM - 351

Computer Assignment 3 Due 1/19/05 Use Minitab to do this problem 1.The probability that a randomly selected joint from a large lot is defective is .361 A welder is about to weld 92 joints. Use Minitab to find the probability that A. at most forty two

Arizona - CS - 127

Chapter 5Analysis of AlgorithmsGoals Analyze algorithms Understand some classic searching and sorting algorithms Distinguish runtime order: O(1), O(n), O(n log n), and O(n2)5.1 Algorithm AnalysisThis chapter introduces a way to investigate t

RIT - SMAM - 351

SMAM 351Exam 4Name_1. The length of time in minutes for an individual to be served at a cafeteria is has probability density function f(x) = .25e .25x ,x > 0 A. What is the probability he is served in at most three minutes?(10 points) .25e0

RIT - SMAM - 351

SMAM 351 Homework 1 Solution Due 12/6/04 1. Consider the sample space S of all aircraft types that land at the Rochester Monroe County Airport. Let A be the aircraft is propeller driven, B be the event the aircraft carries 50 or fewer passengers, C b

RIT - SMAM - 351

#3 Due 1/3/05 1. A Texas based company keeps trained crews on call to fight oil fires anywhere in the world. The company has five crews on call and the probabilities of calls in a week are given in the table below. Number of calls (N) 0 1 2 3 4 5 Pro

RIT - SMAM - 351

#4 Due 1/10/05 1. Four in ten Americans who travel by car look for food and gas outlets visible from the highway. Suppose a random sample of n = 25 Americans who travel by car are asked how they determine where to stop for food and gas. Let x be the

RIT - SMAM - 351

#5 Due 1/17/04 1. The total number of hours measured in units of 100 hours that a family watches television over a period of one year is a continuous random variable with probability density function1 25 x 1 f ( x )= 25 (10 x) 0 0< x < 5 5 < x

RIT - SMAM - 351

#8 Due 2/7/04 1.Let X denote the number of times a certain numerical control machine will malfunction 1, 2 or 3 times on any given day. Let Y denote the number of times a technician is called in on an emergency call. The joint probability distributio

RIT - SMAM - 351

#9 Due 2/14/05 1. Suppose discrete random variables X and Y have the joint probability mass function y / x 3 0 3 2 0 .35 0 0 .25 0 .25 2 0 .15 0 x 3 0 3 g(x) .25 .50 .25 y 2 0 2 h ( y ) .35 .5 .15 g(3)h(2) (.25)(.15) 0 = EX = 0 EY = 0 EXY = 0 cov(X,

RIT - SMAM - 351

SMAM 351 Worksheet 1 1.Three equally qualified runners John, Bill and Dave run a 100 meter sprint and the order of finish is recorded. A. How many simple events are in the sample space? Enumerate them.B. What is the probability of each event?C. W

RIT - SMAM - 351

SMAM 351Worksheet 3Name_1. Consider the probability mass function f(x) = (8/7)(1/2) x.x = 1,2,3 Find A P(X 2) B. The mean variance and the standard deviation.C. The cumulative distribution function.2. The probability of successfully landin

RIT - SMAM - 351

SMAM 351Worksheet 4Name_1. Given the continuous function f(x) = k(1+ 2x),0 < x < 2 A. Determine k so that f(x) is a pdf.B. Find the CDFC. Find P(.5 < X < 1.5)D. Find the mean, median, variance and standard deviation of f(x)2. The cumula

Cornell - CS - 100

/ helloworld David I. Schwartz, 1/2000/ task: say hellopublic class helloworld { public static void main(String[] args) { / say hiSystem.out.println("Hello, world!");/ Try the following:/ System.out.print("Hello, world!\n");/ What

Cornell - CS - 100

/ area1: David I. Schwartz 1/2000/ find area of circlepublic class area1 { public static void main(String[] args) {/ Declare radius r and area A/ A and r will store floating-point valuesdouble r;double A;/ Assign a f-p value to r

Cornell - CS - 100

/ types: David I. Schwartz 1/2000/ demonstrate variety of types and literalspublic class types { public static void main(String[] args) {int i;/ declare integer ii = 1+1;/ assign 1 to ifloat f;/ declare floating-point ff = 1f/3f;

Cornell - CS - 100

/ area2: David I. Schwartz 2/1/2000/ find area and perimeter of circleimport java.text.DecimalFormat;public class area2 { public static void main(String[] args) {/*/ Set up TokenReader to obtain input:/*TokenReader in = new TokenRe

Cornell - CS - 100

2/1/2000Thomas Yan-suppose int variables a, b, c have been assigned values.here are various attempts to print the maximum value,with some questions for you to think about.we recommend that you hand-trace and then actually run eachprogram segm

Cornell - CS - 100

public class CUCSApplication { static void main(String[] args) { TokenReader in = new TokenReader(System.in); int a, b, c; System.out.print("please enter a: "); a = in.readInt(); System.out.print("please en

Cornell - CS - 100

From: tyan@cs.cornell.edu (Thomas Yan)Newsgroups: cornell.class.cs100Subject: Idiom for swapping two variablesDate: 2 Feb 2000 20:05:05 GMTin section last week, you should have seen this idiom (common, well-known code sequence) for swappingtwo

Cornell - CS - 100

/ $%$ is the remainder operation, e.g./ 15 divided by 2 is 7 with remainder 1, so 15 % 2 = 1, and/ 1 divided by 2 is 0 with remainder 1, so 1 % 2 = 1, and/ 16 divided by 2 is 8 with remainder 0, so 16 % 2 = 0. int n = 19; int x = 0; int y =

Cornell - CS - 100

this table illustrates how code for echoing, printing the max, andprinting the average of a sequences of grades, terminated by -1, allfit into the template/pattern we have given for processing an inputsequence.note:+ view this in a mono-spaced

Cornell - CS - 100

/*The operator $%$ is used to compute the remainder $a%b$ ofdividing an integer $a$ modulo (by) a non-zero integer $b$.you might have seen early in school things like "17 divided by 5 is 3 remainder 2", perhaps written "3 r 2".the remainder 2 i

Cornell - CS - 100

/ shortcuts for operatorspublic class increment_ops { public static void main(String[] args) {int a,b;/ Without assigning to another variablea = 0;a+;System.out.println("a+ = " + a);a = 0;+a;System.out.println("+a = " + a);

RIT - SMAM - 351

SMAM 351 Worksheet 6 Name_ 1. The joint probability mass function of discrete random variables X and Y is given in the table below. y p(x,y) 0 1 2 0 .10 .04 .02 x 1 .08 .20 .06 2 .06 .14 .30 Find A. P[X = Y] =.60B. f(x|1) x 0 4 f (x|1) 381 20 38

Cornell - CS - 100

/ Count loops: 2/9/2k DIS/ Reprompt user for inputpublic class reprompt2 { public static void main(String[] args) {/-/ Setup/--TokenReader in = new TokenReader(System.in);int val = 0;int count = 0;boolean test;/-/ Prompt fo

Cornell - CS - 100

/ user input/ what to do if input is wrongpublic class prompt_user { public static void main(String args[]) {/ enable inputTokenReader in = new TokenReader(System.in);/ Exiting program entirely:System.out.print("Test #1: Enter intege

Cornell - CS - 100

/ Print analyze table: 2/9/2K DIS/ nested loopspublic class nested1 { public static void main(String[] args) {int a,amin,amax;int b,bmin,bmax;amin = 0;amax = 4;bmin = 1;bmax = 7;System.out.println();/ Outer loopa = amin;

Cornell - CS - 100

/ Print analyze table: 2/9/2K DIS/ nested loops (condensed version)public class nested2 { public static void main(String[] args) {int amin = 0;int amax = 4;int bmin = 1;int bmax = 7;System.out.println();for(int a = amin; a <= am

Cornell - CS - 100

/ Write a program to print the row and column indices of each/ cell of an M x N matrix// Example for M = 3, N = 4 print out:/ 11 12 13 14/ 21 22 23 24/ 31 32 33 34// MatrixLabels1 and MatrixLabels2 both solve this problem using/ while loops,

Cornell - CS - 100

/ Write a program to print the row and column indices of each/ cell of an M x N matrix// Example for M = 3, N = 4 print out:/ 11 12 13 14/ 21 22 23 24/ 31 32 33 34// MatrixLabels1 and MatrixLabels2 both solve this problem using/ while loops,

Cornell - CS - 100

/ Write a program that prints the first n positive integers that/ are evenly divisible by at least 5 positive integers.// Example: n = 10/ Desired output: 12 16 18 20 24 28 30 32 36 40public class DivisibleBy5 { public static void main

Cornell - CS - 100

/ methods1 DISclass Test { int i; int j = 1; void print() {System.out.println("i: " + i);System.out.println("j: " + j); } int data(int a, int b) {i += a;j += b;return i+j; }}public class methods1 { pu

Cornell - CS - 100

/ methods2 DIS/ testing default values of instance variableclass Test { int i; / is default value 0? void print() {System.out.println("i: " + i);} void data(int a) {i += a;}}public class methods2 { public static void main(String

Cornell - CS - 100

/ methods3 DIS/ scopeclass Test { int A; void print(int A) {System.out.println("Inst. A: " + this.A);System.out.println("Local A: " + A); }}public class methods3 { public static void main(String[] args) {Test A = new T

Cornell - CS - 100

/ methods4 DIS/ print vs returnclass Test { int x; int add(int y) {return x+y; }}public class methods4 { public static void main(String[] args) {Test t = new Test();/ return a value/ note: nothing prints!int a = t.a

Cornell - CS - 100

/ null0 DIS/ instance variables as references default to null refclass Person { int k; Person a; void data() {if (a=null) System.out.println("nothing to do");else System.out.println("something to do"); }}public cl

Cornell - CS - 100

/ A program that uses straight lines to draw around the/ outline of a circle. Given a circle, draw a line between/ two points on the circle separated by a certain angle. -AMHimport java.awt.*;class Drawing2 extends Frame { / Constructor: set