For Example 6.15, the keen reader may have wondered why use a Poisson distribution to find probabilities, instead of the empirical probabilities. The table below presents the empirical probabilities.

a) What is the empirical probability that X = 3?
b) What is the empirical probability that X ≥ 6?
c) If X ∼ Poisson(4.03), find P(X = 3) and compare with (a).
d) If X ∼ Poisson(4.03), find P(X ≥ 6) and compare with (b).

Example 6.15 As of 2016, it is estimated that almost four million people live in the city of Los Angeles. Last year (365 days) records from an emergency room were used to evaluate the number of heart attack cases that were treated each day. Figure 6.7 illustrates the probability distribution of the collected data. Emergency staff would like to determine the probability of having 6 heart attack cases or more.

Transcribed Image Text:

X 0 1 2 3 4 5 6 7 8 9 P(X x) 0.0137 0.0548 0.1589 0.2219 0.1836 0.1562 0.0959 0.0548 0.0356 0.0192 =