Lecturenotes15

Lecturenotes15 - STAT 430/510 Lecture 15 STAT 430/510 Probability Hui Nie Lecture 15 June 23rd 2009 STAT 430/510 Lecture 15 Sum of Independent

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Unformatted text preview: STAT 430/510 Lecture 15 STAT 430/510 Probability Hui Nie Lecture 15 June 23rd, 2009 STAT 430/510 Lecture 15 Sum of Independent Normal R.V. If X i , i = 1 , ··· , n , are independent random variables that are normally distributed with respective parameters μ i , σ 2 i , i = 1 , ··· , n , then ∑ n i = 1 X i is normally distributed with parameters ∑ n i = 1 μ i and ∑ n i = 1 σ 2 i . STAT 430/510 Lecture 15 Example A basketball team will play a 44-game season. Twenty-six of these games are against class A teams and 18 are against class B teams. Suppose that the team will win each game against a class A team with probability 0.4 and will win each game against a class B team with probability 0.7. Suppose also that the results of the different games are independent. Approximate the probability that (a) the team wins 25 games or more; (b) the team wins more games against class A teams than it does against class B teams. STAT 430/510 Lecture 15 Example: Solution Let X A and X B respectively denote the number of games the team wins against class A and class B teams....
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This note was uploaded on 06/28/2009 for the course STAT 430 taught by Professor Krieger during the Summer '08 term at UPenn.

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Lecturenotes15 - STAT 430/510 Lecture 15 STAT 430/510 Probability Hui Nie Lecture 15 June 23rd 2009 STAT 430/510 Lecture 15 Sum of Independent

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