lec4.3

# lec4.3 - 72 Lecture 7 CHAPTER 4 COMMONLY USED DISTRIBUTIONS...

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72 Lecture 7: CHAPTER 4: COMMONLY USED DISTRIBUTIONS The Binomial Distribution – Cont’d (Section 4.2, page 202) THE BINOMIAL DISTRIBUTION – (discrete) Recall: p(x) = proportion of batches with x S’s (successes) Summary for Binomial Distribution: The Mean and Variance of a Binomial Random Variable Summary: If ) , ( ~ n Bin X , then the mean and variance of X are given by n x ) 1 ( 2 n x If a total of n trials are conducted, and The trials are independent Each trial has the same success probability X is the number of successes in the n trials then X has the binomial distribution with parameters n and , denoted ) , ( ~ n Bin X

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73 Our first PROOF! Proof: We obtain the mean of the binomial distribution:
74 Proof: We obtain the variance of the binomial distribution:

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75
76 Example (revisited): A large industrial firm allows a discount on any invoice that is paid within 30 days. Of all invoices, 10% receive the discount. In a company audit, 12 invoices are sampled at random. (i)

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lec4.3 - 72 Lecture 7 CHAPTER 4 COMMONLY USED DISTRIBUTIONS...

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