1. In addition to the d and p functions mentioned in class, R includes q and r functions. What do these do? Explore the help files.
  2. Austria had a birth rate of approximately 9.9 births per 1000 people in 2019. Assume this rate is constant over the year, and that all births are independent.
    1. For a randomly selected cohort of 1000 people, what is the probability of observing exactly 11 births over a 1-year period?
    2. What about observing 11 or more births?
  3. Is a probability density the same as a probability?
    1. Human height is normally distributed within populations. From 1980-1994 within 20 wealthy countries, mean female height was 164.7 cm, with a standard deviation of 7.1 cm. What is the maximum probability density of this normal distribution, and what is the x-value \(x_{max}\) at which maximum probability density occurs?
    2. What is the probability that a female in this time period has a height exactly equal to \(x_{max}\)
    3. If the maximum probability density and the \(pr(x_{max})\) are not the same, why not? Do these answers make sense?
    4. What is the probability that a woman has a height in the range \(x_{max} \pm 3\)
  4. For the same distribution, what is the 40th percentile for height? In other words, what is the value \(x\) such that the probability of observing x or less is 0.4? — \(pr(X \le x) = 0.4\)
    1. What is \(x\) if \(pr(X > x) = 0.4\)?