Birth Order - The 2012 National Vital Statistics Report Provides information on how the nearly four million live births that occurred in 2011 broken down by birth order. Choose at random a baby born in America in 2011: Birth Order X 1 2 3 4 5 6 7 P(X) 0.43 0.25 0.19 0.06 0.03 0.02 0.02 a)As defined here, is the random variable X discrete or continuous? Does it Satisfy requirements for a legitimate probability model? Why? b)Describe in words the event P( X ≥ 4). What is its probability? c)Write the event “a woman gives birth in 2011 to her first through fourth child" in terms of X. What is the probability of this event?
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!
Birth Order - The 2012 National Vital Statistics Report Provides information on how the nearly four million live births that occurred in 2011 broken down by birth order. Choose at random a baby born in America in 2011:
| Birth Order X |
1 | 2 | 3 |
4 | 5 |
6 | 7 | |
| P(X) | 0.43 | 0.25 | 0.19 | 0.06 | 0.03 | 0.02 | 0.02 |
a)As defined here, is the random variable X discrete or continuous? Does it Satisfy requirements for a legitimate probability model? Why?
b)Describe in words the
c)Write the event “a woman gives birth in 2011 to her first through fourth child" in terms of X. What is the probability of this event?
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