Lecture 10 - O blood 2 Binomial Distribution Suppose X ~...

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Lecture 10 Material Covered in This Lecture: 1 C Chapter 5, Section 5.1: Sampling Distribution for Counts and Proportions The binomial distribution for sample counts
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Let X = # of success. The distribution of the count X of successes in the binomial setting is called binomial distribution. Notation: X~B(n,p) Question 1: What are the possible values of X? Question 2: What are the corresponding probabilities? Example 1 (Example 5.2, p.336) : In each of the following cases, is X a binomial random variable or not? 1 (a) Toss a balanced coin 10 times and count the number X of heads. 2 (b) Deal 10 cards from a shuffled deck and count the number X of red cards. 3 (c) Genetics says that children receive genes from their parents independently. Each child of a particular pair of parents has probability 0.25 of having type O blood. These parents have 5 children, let X be the number of child who has
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Unformatted text preview: O blood. 2. Binomial Distribution Suppose X ~ B(n,p). The possible values can be taken by X is 0, 1, 2, …, n. Then what is P(X=k), k=0, 1, …, n ? Two methods to find P(X=k), k=0,1,…,n. (1). Using Minitab. (2). Using Table (for 2 ≤ n ≤ 20). (3)Using formula Example 2: Rolling a fair die 10 times. Let X = # of 6. Then X ~ B(10, 1/6). Find P(X=k), k=0,1,2,3,4,5,6,7,8,9,10, and P(X≤ 4) Example 3 ( Example 5.2 continued, p.336 ): Consider (c). Find P(X=k),k=0,1,2,3,4,5, and P(X>3). Example4(example5.5) 3. Mean and Standard Deviation of the Binomial Distribution Proof: Example 4: Rolling a fair die 10 times. Let X = # of 6. Compute the mean and the standard deviation. Example 5 (Example 5.2 continued, p.336) : Consider (c). Compute the mean and the standard deviation. If time? Do Exercise 5.2, 5.12. HW:5.1, 5.3, 5.5, 5.6, 5.13,...
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This note was uploaded on 07/25/2008 for the course STT 421 taught by Professor Nane during the Summer '08 term at Michigan State University.

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Lecture 10 - O blood 2 Binomial Distribution Suppose X ~...

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