I'm trying to solve the following problem. It's actually answered in the book but I couldn't really figure it out.
Suppose a determination of bacteriuria-bacteria in urine- has been made over a large population of women at one in time and 5% of those sampled are positive for bacteriuria.
One interesting phenomenon that there is a turnover which means if bacteria is measured on the same woman at two different points in time , the result 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), whereras only 4.2 of women who were not bacteriuric at time 0 are bacteriuric at time 1. Let X be the randome variable representing the number of bacteriuric events over two time periods for 1 women and still assume probability that a women will be positive for bacteriuria at any one time is 5%
a- What is the probability distribution of X?
b- What is the mean of X?
c- What is the variance of X?
This question seems Poisson dist.
We have p=.05
My problem I couldn’t figure out Lamda from the question:
I tried to find lamda in order to apply Poisson formula, but I failed
5% 0f population are positive meaning 5 women are sick
Now 20% of5 is one.
The book answers are
a- P(X=0)=.91
P(X=1)=.08
P(X=2)=.01
b- .100
c- .110
Can anybody help
Suppose a determination of bacteriuria-bacteria in urine- has been made over a large population of women at one in time and 5% of those sampled are positive for bacteriuria.
One interesting phenomenon that there is a turnover which means if bacteria is measured on the same woman at two different points in time , the result 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), whereras only 4.2 of women who were not bacteriuric at time 0 are bacteriuric at time 1. Let X be the randome variable representing the number of bacteriuric events over two time periods for 1 women and still assume probability that a women will be positive for bacteriuria at any one time is 5%
a- What is the probability distribution of X?
b- What is the mean of X?
c- What is the variance of X?
This question seems Poisson dist.
We have p=.05
My problem I couldn’t figure out Lamda from the question:
I tried to find lamda in order to apply Poisson formula, but I failed
5% 0f population are positive meaning 5 women are sick
Now 20% of5 is one.
The book answers are
a- P(X=0)=.91
P(X=1)=.08
P(X=2)=.01
b- .100
c- .110
Can anybody help