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MATH408: Probability & Statistics Summer 1999 WEEK 4

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Dr. Srinivas R. Chakravarthy

Professor of Mathematics and Statistics

Kettering University

(GMI Engineering & Management Institute)

Flint, MI 48504-4898

Phone: 810.762.7906

Email: schakrav@kettering.edu

Homepage: www.kettering.edu/~schakrav

PROBABILITY MASS FUNCTION

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

BINOMIAL (cont’d)

- 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 =

Graph of Poisson PMF

EXPONENTIAL DISTRIBUTION

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

X is exponentially distributed

- 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.

- 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.

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.