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The Binomial Distribution

The Binomial Distribution. Bernoulli Process Repeated, independent trials Two outcomes: “Success” and “Failure” Invariant probability of success:  The random variable is the number of successes in n trials. The binomial formula for the probability of x successes in n trials:

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The Binomial Distribution

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  1. The Binomial Distribution • Bernoulli Process • Repeated, independent trials • Two outcomes: “Success” and “Failure” • Invariant probability of success:  • The random variable is the number of successes in n trials

  2. The binomial formula for the probability of x successes in n trials: EXAMPLE: Find the probability of 4 successes in 12 trials if  = 0.32.

  3. Example: 12% of the switches in a large shipment are defective. In a sample of 15 switches, what is the probability that • Exactly three are defective • At least two are defective • Example: 20% of the memory chips in a production run are defective. In a sample of 16 chips, what is the probability that • Exactly four are defective • Five or more are defective

  4. The Binomial Tables • Page 887 and ff. • Table A1: individual values • Table A2: cumulative values, P(x  k)

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