MATH408: Probability & Statistics Summer 1999 WEEK 4

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MATH408: Probability & Statistics Summer 1999 WEEK 4. Dr. Srinivas R. Chakravarthy Professor of Mathematics and Statistics Kettering University (GMI Engineering & Management Institute) Flint, MI 48504-4898 Phone: 810.762.7906 Email: [email protected]

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MATH408: Probability & StatisticsSummer 1999WEEK 4

Dr. Srinivas R. Chakravarthy

Professor of Mathematics and Statistics

Kettering University

(GMI Engineering & Management Institute)

Flint, MI 48504-4898

Phone: 810.762.7906

Email: [email protected]

Homepage: www.kettering.edu/~schakrav

Example 3.16

Verify that  = 0.4 and  = 0.6

BINOMIAL RANDOM VARIABLE

p

defect

Good

q

• n, items are sampled, is fixed
• P(defect) = p is the same for all
• independently and randomly chosen
• X = # of defects out of n sampled
POISSON RANDOM VARIABLE
• Named after Simeon D. Poisson (1781-1840)
• Originated as an approximation to binomial
• Used extensively in stochastic modeling
• Examples include:
• Number of phone calls received, number of messages arriving at a sending node, number of radioactive disintegration, number of misprints found a printed page, number of defects found on sheet of processed metal, number of blood cells counts, etc.
POISSON (cont’d)

If X is Poisson with parameter , then  =  and 2 = 

MEMORYLESS PROPERTY

P(X > x+y / X > x) = P( X > y)

 X is exponentially distributed

Normal approximation to binomial(with correction factor)
• Let X follow binomial with parameters n and p.
• P(X = x) = P( x-0.5 < X < x + 0.5) and so we approximate this with a normal r.v with mean np and variance n p (1-p).
• GRT: np > 5 and n (1-p) > 5.
Normal approximation to Poisson (with correction factor)
• Let X follow Poisson with parameter .
• P(X = x) = P( x-0.5 < X < x + 0.5) and so we approximate this with a normal r.v with mean  and variance .
• GRT:  > 5.
HOME WORK PROBLEMS(use Minitab)

Sections: 3.6 through 3.10

51, 54, 55, 58-60, 61-66, 70, 74-77, 79, 81, 83, 87-90, 93, 95, 100-105, 108

• Group Assignment: (Due: 4/21/99)
• Hand in your solutions along with MINITAB output, to Problems 3.51 and 3.54.