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*4.37 What is the variance of X?

*4.37 What is the variance of X?

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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Please only answer 4.37
Renal Disease The presence of bacteria in a urine sample (bacteriuria) is sometimes associated with symptoms of kidney disease in women. Suppose a determination of bacteriuria has been made over a large population of women at one point in time and 5% of those sampled are positive for bacteriuria. *4.33 If a sample size of 5 is selected from this population, what is the probability that 1 or more women are positive for bacteriuria? *4.34 Suppose 100 women from this population are sam- pled. What is the probability that 3 or more of them are positive for bacteriuria? One interesting phenomenon of bacteriuria is that there is a "turnover"; that is, if bacteriuria is measured on the same woman at two different points in time, the results are not necessarily the same. Assume that 20% of all women who are bacteriuric at time 0 are again bacteriuric at time 1 (1 year later), whereas only 4.2% of women who were not bacteriuric at time 0 are bacteriuric at time 1. Let X be the random variable representing the number of bacteriuric events over the two time periods for 1 woman and still as- sume that the probability that a woman will be positive for bacteriuria at any one exam is 5%. *4.35 What is the probability distribution of X? *4.36 What is the mean of X? *4.37 What is the variance of X?
Transcribed Image Text:Renal Disease The presence of bacteria in a urine sample (bacteriuria) is sometimes associated with symptoms of kidney disease in women. Suppose a determination of bacteriuria has been made over a large population of women at one point in time and 5% of those sampled are positive for bacteriuria. *4.33 If a sample size of 5 is selected from this population, what is the probability that 1 or more women are positive for bacteriuria? *4.34 Suppose 100 women from this population are sam- pled. What is the probability that 3 or more of them are positive for bacteriuria? One interesting phenomenon of bacteriuria is that there is a "turnover"; that is, if bacteriuria is measured on the same woman at two different points in time, the results are not necessarily the same. Assume that 20% of all women who are bacteriuric at time 0 are again bacteriuric at time 1 (1 year later), whereas only 4.2% of women who were not bacteriuric at time 0 are bacteriuric at time 1. Let X be the random variable representing the number of bacteriuric events over the two time periods for 1 woman and still as- sume that the probability that a woman will be positive for bacteriuria at any one exam is 5%. *4.35 What is the probability distribution of X? *4.36 What is the mean of X? *4.37 What is the variance of X?
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