9_23_11

9_23_11 - Binomial Distribution Instructor: Andrew Liu...

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Unformatted text preview: Binomial Distribution Instructor: Andrew Liu September 23, 2011 Textbook sections: 3-6 Binomial Distribution: Some Motivating Examples E.g.1 A fair coin. Let 1 head, 0 tail. Suppose we toss 10 times. Define a random variable X : the number of heads appeared. What is P ( X = 5)? Textbook sections: 3-6 Binomial Distribution: Some Motivating Examples E.g.1 A fair coin. Let 1 head, 0 tail. Suppose we toss 10 times. Define a random variable X : the number of heads appeared. What is P ( X = 5)? E.g.2 A multiple choice test contains 10 questions, each with 4 choices. Suppose you have absolutely no knowledge of the subject and purely guess (i.e., you have 1 4 chance of guessing the question right). Let X denote the number of questions you answered correclty. What is P ( X = 8)? Textbook sections: 3-6 Binomial Distribution: Some Motivating Examples E.g.1 A fair coin. Let 1 head, 0 tail. Suppose we toss 10 times. Define a random variable X : the number of heads appeared. What is P ( X = 5)? E.g.2 A multiple choice test contains 10 questions, each with 4 choices. Suppose you have absolutely no knowledge of the subject and purely guess (i.e., you have 1 4 chance of guessing the question right). Let X denote the number of questions you answered correclty. What is P ( X = 8)? E.g.3 In the next 30 births at a hospital, let X denote the number of female birth. What is P ( X = 20) (assume equal probabilities of a male and a female birth)? Textbook sections: 3-6 Bernoulli Trial Similarities among the previous examples: Repetition of a single experiment (called a trial) Textbook sections: 3-6 Bernoulli Trial Similarities among the previous examples: Repetition of a single experiment (called a trial) The trials are independent Textbook sections: 3-6 Bernoulli Trial...
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9_23_11 - Binomial Distribution Instructor: Andrew Liu...

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