ECE 3077 Problem - You work for the local power generation company BuzzPower (BP)

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. What are the maximum likelihood