N independent trials are to be conducted, each with "success" probability p. Let X; = 1 if trial i is a success and X; = 0 if it is not. What is the distribution of the random variable X = X1+X2+...+XN? Express Pla < X

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.3: Binomial Probability
Problem 2E: If a binomial experiment has probability p success, then the probability of failure is...
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. QUESTION:
N independent trials are to be conducted, each with "success" probability p. Let X; = 1 if trial i is a
success and X; = 0 if it is not. What is the distribution of the random variable X = X1+X2+...+XN?
Express Pla < X < b) as a sum (where a <b and these are integers between 0 and N). Use the central
limit theorem to provide an approximation to this probability. Compare your approximation with the
limit theorem of De Moivre and Laplace on pl189 of Kreyszig.
%3D
Transcribed Image Text:. QUESTION: N independent trials are to be conducted, each with "success" probability p. Let X; = 1 if trial i is a success and X; = 0 if it is not. What is the distribution of the random variable X = X1+X2+...+XN? Express Pla < X < b) as a sum (where a <b and these are integers between 0 and N). Use the central limit theorem to provide an approximation to this probability. Compare your approximation with the limit theorem of De Moivre and Laplace on pl189 of Kreyszig. %3D
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