Probability Distributions u Discrete Probability Distribution –Discrete vs. continuous random variables »discrete - only a countable number of values »continuous.

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Presentation transcript:

Probability Distributions u Discrete Probability Distribution –Discrete vs. continuous random variables »discrete - only a countable number of values »continuous - any value in an interval –distribution is a table, graph, or formula that gives the probability of observing each value of x.

u Binomial Distribution –Conditions (see p.270) »1. n units sampled from population with replacement »2. Either success or failure »3. Probability of success is  »4. Independent samples »5. Binomial random variable: x = successes –distribution –mean, variance »  = n  »  2 = n  (1-  )

u Applications –Weekly compliance sampling »agency wants compliance 95% of time »52*0.05 = 2.6 »agency will allow only 2 violations per year, any more and they’ll shut you down »you run your operation at 95% compliance, what are your odds of being shut down?

u Poisson Distribution –Rare event –characteristics (283) »# of times an even occurs during a unit »prob same for all units »# in one unit independent of others –distribution –Long-term average of 6 accidents per year at intersection »probability of exactly 6 this year »probability of 3 or less »after improvements, had only 2 accidents. Did the improvements help.

u False positive example –In a blood test, you test positive for the presence of the HIV virus. Should you be concerned? »Test is 99% accurate »1 out of 1000 people have HIV »Out of 100,000 u # of false positives = u # of true positives =