# MATHEMATICS

You work for the local power generation company BuzzPower (BP), which owns two large generators. The most important factor determining how many generators they need to run to meet demand is the weather (due to air conditioning usage). If X is a random variable denoting the high temperature today, a meteorological model assigns the following
probabilities:

see attached file

If Y {1, 2} is a random variable denoting the number of generators that must be used,
BP knows from past history that the number of required generators follows the following
probabilities that depend on the high temperature. In particular, BP’s model says that:
Pr(Y = 1|X = x) = (82 − x) / 4 for x 2 {79, 80, 81}.

1. What is the probability of BP using two generators today?

2. What is the expected number of generators BP will use today?

3. You haven’t been outside today, but you know 1 generator is running. Wha

Fizz Laboratories, a pharmaceutical company, has developed a new pain-relief medication. Sixty patients suffering from arthritis and needing pain relief are available. Each patient will be treated and asked an hour later, “About what percentage of pain relief did you experience?”

1. Why should Fizz not simply administer the new drug and record the patients’ responses?
2. Outline and design an experiment to compare the drug’s effectiveness with that of aspirin and of a placebo.
3. Should patients be told which drug they are receiving? How would this knowledge probably affect their reactions?
4.  If patients are not told which treatment they are receiving, the experiment is single-blind. Should this experiment be double-blind also? Explain.

t are the maximum likelihood

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