Team Assignment 6 An optical inspection system is

Team Assignment 6 An optical inspection system is

Team Assignment 6 An optical inspection system is used to distinguish among different part types. The probability of a correct classification is 0.98. Suppose that three parts are inspected and that the classifications are independent. Let the random variable X denote the number of parts correctly classified. a) Determine the probability mass function of X. b) Find the mean, E(X). c) Find the standard deviation of X. 1

Solution Let Ri be the event that part i classified correctly. Let Wi be the event that part i classified incorrectly (i.e., the classification is wrong). 2 Solution: Part a P( X 0) P(W1W2W3 ) (0.02)(0.02)(0.02) (0.02)3 . P( X 1) P( R1W2W3 ) P(W1 R2W3 )

P(W1W2 R3 ) (0.98)(0.02)(0.02) (0.02)(0.98)(0.02) (0.02)(0.02)(0.98) (3)(0.98)(0.02) 2 . P( X 2) P( R1 R2W3 ) P( R1W2 R3 ) P(W1 R2 R3 ) (0.98)(0.98)(0.02) (0.98)(0.02)(0.98) (0.02)(0.98)(0.98) (3)(0.98) 2 (0.02). P( X 3) P( R1 R2 R3 ) (0.98)(0.98)(0.98) (0.98)3 .

3 Solution: Part a f (0) P ( X 0) (0.02)3 f (1) P ( X 1) (3)(0.98)(0.02) 2 f (2) P ( X 2) (3)(0.98) 2 (0.02) f (3) P ( X 3) (0.98)3 4 Solution: Part b 3 xf ( x)

x 0 (0)( f (0)) (1)( f (1)) (2)( f (2)) (3)( f (3)) (1)((3)(0.98)(0.2) 2 ) (2)((3)(0.98) 2 (0.2)) (3)(0.98)3 2.94. 5 Solution: Part c 3 V ( X ) x 2 f ( x) 2 x 0

(02 )( f (0)) (12 )( f (1)) (22 )( f (2)) (32 )( f (3)) 2.942 (1)((3)(0.98)(0.2) 2 ) (4)((3)(0.98) 2 (0.2)) (9)(0.98)3 8.6436 0.0588 V (X ) 0.0588 0.2425 6

Recently Viewed Presentations

  • EBP LANGUAGE GROUP 2009 - WordPress.com

    EBP LANGUAGE GROUP 2009 - WordPress.com

    Semantic Feature Analysis. Aphasia is frequently associated with semantic breakdown . Semantic feature analysis is a technique that underpins the general philosophy behind many treatments for semantic impairments
  • Being an Effective Leader - Sacramento State

    Being an Effective Leader - Sacramento State

    Turnover is low, Average tenure is 10 years 50% staff experienced career progression in past two years High levels of satisfaction after leadership training Being an Effective Leader Satya Tiwari Steve Greeley Julien Moua Christine Kenney Being an Effective Leader...
  • Management 9e.- Robbins and Coulter

    Management 9e.- Robbins and Coulter

    Define the six important employee behaviors that managers want to explain, predict, and influence. 13.2 Attitudes and Performance. Describe the three components of an attitude. Describe the impact job satisfaction has on employee behavior.
  • Specific Behavioral Health Issues that Affect Medical Conditions

    Specific Behavioral Health Issues that Affect Medical Conditions

    Conclusions A modest association of baseline depressivesymptoms with incident type 2 diabetes existed that was partiallyexplained by lifestyle factors. Impaired fasting glucose anduntreated type 2 diabetes were inversely associated with incidentdepressive symptoms, whereas treated type 2 diabetes showeda positive association...
  • Dyslexia Intervention: Key to Achieving Utah's Education Goals

    Dyslexia Intervention: Key to Achieving Utah's Education Goals

    The Dyslexic Brain "Because of dyslexia, my brain works differently, and I can see these patterns. I do have a gift that other people don't have, and I will always stay ahead of the crowd and see more in an...
  • Iowa Government Finance Initiative: Updates

    Iowa Government Finance Initiative: Updates

    Advanced financial analysis. Economic base analysis. Demographic analysis. Economic Impact Studies. Feasibility Studies. Benefit-Cost Analysis. Retail Trade Analysis. Housing (affordability, adequacy, supply-demand, needs assessment)
  • Eastern Europe - Sayre Geography Class

    Eastern Europe - Sayre Geography Class

    Palace of the Parliament Palace balcany Unirii Romania Peles Castle Sinaia, Romania is a romantic castle placed in an idyllic setting in the Carpathian Mountains, near Sinaia, in Prahova County, Romania, on an existing medieval route linking Transylvania and Wallachia,...
  • 19/03/20 Compounds and Mixtures Elements 19/03/20 If a

    19/03/20 Compounds and Mixtures Elements 19/03/20 If a

    Compounds and Mixtures * Elements If a solid, liquid or gas is made up of only one type of atom we say it is an element. For example, consider a tripod made up of iron: These atoms are ALL iron...