Could anyone add some insight on this one for me? I've been going nowhere fast, though I sped through the rest of the homework.
One interesting phenomena of bacteriuria is that there is a “turnover”; that is, if bacteriuria is measured on the same woman at 2 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 2 time periods for 1 woman and assume that the probability that a woman will be
positive for bacteriuric at any one exam is 5% (i.e. prevalence is 5%). Note also that the two examination results for the same woman will NOT be independent.
a) What is the probability distribution of X?
b) What is the mean of X?
c)What is the variance of X?
One interesting phenomena of bacteriuria is that there is a “turnover”; that is, if bacteriuria is measured on the same woman at 2 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 2 time periods for 1 woman and assume that the probability that a woman will be
positive for bacteriuric at any one exam is 5% (i.e. prevalence is 5%). Note also that the two examination results for the same woman will NOT be independent.
a) What is the probability distribution of X?
b) What is the mean of X?
c)What is the variance of X?