Let X1, X2,...X100 be the annual average temperature in Paris in the years 2001, 2002, ..., 2100, respectively. Assume that average annual temperatures are sampled i.id. from a continuous distribution.(Note: For this problem, we assume the temperature distribution doesn't change over time. With global warming, this is not a good assumption.)A year is a record high if its average temperature is greater than those in all previous years (starting with 2001), and a record low if its average temperature islower than those in all previous years. By definition, the year 2001 is both a record high and a record low.1. In the 20 century (the years 2001 through 2100, inclusive), find the expected number of years that are either a record high or a record low.2. Let N be an r.v. representing the number of years required to get a new record high after the year 2001. Find P(N > n) for all positive integers n, and use thisto find the PMF of N.3. Check answers to parts (1) and (2).4. Explain how you could use this model to determine whether or not global warming is really happening.
Let X1, X2,...X100 be the annual average temperature in Paris in the years 2001, 2002, ..., 2100,
respectively. Assume that average annual temperatures are sampled i.id. from a continuous distribution.
(Note: For this problem, we assume the temperature distribution doesn't change over time. With global warming, this is not a good assumption.)
A year is a record high if its average temperature is greater than those in all previous years (starting with 2001), and a record low if its average temperature is
lower than those in all previous years. By definition, the year 2001 is both a record high and a record low.
1. In the 20 century (the years 2001 through 2100, inclusive), find the expected number of years that are either a record high or a record low.
2. Let N be an r.v. representing the number of years required to get a new record high after the year 2001. Find P(N > n) for all positive integers n, and use this
to find the PMF of N.
3. Check answers to parts (1) and (2).
4. Explain how you could use this model to determine whether or not global warming is really happening.
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