1. Uniform Distribution Statistics
The Suez Canal is a vertical straight thoroughfare broken up into three segments:
|Begins at, degrees latitude||Ends at, degrees latitude|
|The Red Sea stretch||29.90||30.17|
|The Great Bitter Lake stretch||30.17||30.80|
|The Mediterranean stretch||30.80||31.26|
The Great Bitter Lake stretch is two-way but the other two stretches are one-way. So, if you make it into a one-way stretch, you’ll cruise through the canal safely. But if you’re caught in the middle stretch when the authorities reverse the traffic in the one-way stretches, you’ll be stranded in the middle of the canal waiting till the traffic is your way again. Ships are distributed uniformly through the canal. Distribution Statistics
(a) Find the probability density of the canal, report its units.
(b) Draw the graphs of the PDF, CDF, and quantile functions for this case. Label the graphs, the axes, and the values you find relevant
(c) What is the probability of being trapped in the middle segment? Find the CDF of the gate between The Red Sea and The Great Bitter Lake. Then find the CDF of the gate between the Great Bitter Lake and the Mediterranean. Then use those values to find your probability.
4. Exponential Distribution Statistics
Boeing 737 is one of the most prolific, oldest, and most polished airliners in the world. In the last 20 years, an airplane of this type has been experiencing 1.2 incidents with more than 50 casualties per year.
Two years ago, the world was bewildered by the two back-to-back crashes of the latest Boeing 737 Max 8 that, together, resulted in more than 300 casualties. Lion Air Flight 610 crashed in October 2018. Ethiopian Airlines Flight 302 crashed in March 2019.
What was the probability that less than five months would pass between the two crashes?
(a) Establish the units in which the length of interval, , is measured in this example. Then, express the long-term average in the same units.
(b) Use the cumulative Distribution Statistics function formula for the exponential distribution to find the probability that x is less or equal to 5.
(c) Draw the probability density function for the problem, point out , , and on it. Indicate what is on the axes.
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