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Problem 14. An important continuous distribution for describing rare events the so-called Poisson Distribution given by the formula f(k; t) = where e Euler's constant. In a binomial distribution problem if n is large and p is close 0, then the probability of k successes Pr(x = k) is approximately f(k;t) with = n · p. This is known as law of small numbers or rare events. In practical oplications, this is a useful fact. For example, if in Problem 3 our drug has non- ficacy p equal 0.1% and n = 1,000, 000, we may use this approximation to make uick calculations concerning the number of patients who will get better on the rug. In this vein, apply this statement to quickly give approximate answers to the

Problem 14. An important continuous distribution for describing rare events the so-called Poisson Distribution given by the formula f(k; t) = where e Euler's constant. In a binomial distribution problem if n is large and p is close 0, then the probability of k successes Pr(x = k) is approximately f(k;t) with = n · p. This is known as law of small numbers or rare events. In practical oplications, this is a useful fact. For example, if in Problem 3 our drug has non- ficacy p equal 0.1% and n = 1,000, 000, we may use this approximation to make uick calculations concerning the number of patients who will get better on the rug. In this vein, apply this statement to quickly give approximate answers to the

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Problem 14. An important continuous distribution for describing rare events is the so-called Poisson Distribution given by the formula f(k; t) = where e is Euler's constant. In a binomial distribution problem if n is large and p is close to 0, then the probability of k successes Pr(x = k) is approximately f(k; t) with t = n· p. This is known as law of small numbers or rare events. In practical applications, this is a useful fact. For example, if in Problem 3 our drug has non- efficacy p equal 0.1% and n = 1, 000, 000, we may use this approximation to make quick calculations concerning the number of patients who will get better on the drug. In this vein, apply this statement to quickly give approximate answers to the following statements: A) The probability that the drug effectively treats all 1 million patients? B) The probability that the drug effectively treats at least three patients? C) The probability that at least 1,000 patients don't get better through the use of the drug (they may get better for other reasons outside the scope of the experiment).
Transcribed Image Text:Problem 14. An important continuous distribution for describing rare events is the so-called Poisson Distribution given by the formula f(k; t) = where e is Euler's constant. In a binomial distribution problem if n is large and p is close to 0, then the probability of k successes Pr(x = k) is approximately f(k; t) with t = n· p. This is known as law of small numbers or rare events. In practical applications, this is a useful fact. For example, if in Problem 3 our drug has non- efficacy p equal 0.1% and n = 1, 000, 000, we may use this approximation to make quick calculations concerning the number of patients who will get better on the drug. In this vein, apply this statement to quickly give approximate answers to the following statements: A) The probability that the drug effectively treats all 1 million patients? B) The probability that the drug effectively treats at least three patients? C) The probability that at least 1,000 patients don't get better through the use of the drug (they may get better for other reasons outside the scope of the experiment).
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