Otitis media is a disease that occurs frequently in the first few years of life and is one of the most common reasons for physician visits after the routine checkup. A study was conducted to assess the frequency of otitis media in the general population in the first year of life. Table 4.15 gives the number of infants of 2500 infants who were first seen at birth who remained disease-free by the end of the ith month of life, i = 0, 1, . . . , 12. (Assume no infants have been lost to follow-up.) Disease-free infants at i the end of month i 0 2500 1 2425 2 2375 3 2300 4 2180 5 2000 6 1875 7 1700 8 1500 9 1300 10 1250 11 1225 12 1200 Suppose an “otitis-prone family” is defined as one in which at least three siblings of five develop otitis media in the first 6 months of life. What proportion of five-sibling families is otitis prone if we assume the disease occurs independently for different siblings in a family?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Otitis media is a disease that occurs frequently in the first
few years of life and is one of the most common reasons
for physician visits after the routine checkup. A study was
conducted to assess the frequency of otitis media in the
general population in the first year of life. Table 4.15 gives
the number of infants of 2500 infants who were first seen at
birth who remained disease-free by the end of the ith month
of life, i = 0, 1, . . . , 12. (Assume no infants have been lost
to follow-up.)
Disease-free infants at
i the end of month i
0 2500
1 2425
2 2375
3 2300
4 2180
5 2000
6 1875
7 1700
8 1500
9 1300
10 1250
11 1225
12 1200
Suppose an “otitis-prone family” is defined as
one in which at least three siblings of five develop otitis media in the first 6 months of life. What proportion
of five-sibling families is otitis prone if we assume the
disease occurs independently for different siblings in a
family?
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