Question 1 A computer program is said to learn from experience E with respect to some task T and some performance measure P if its performance on T, as measured by P, improves with experience E. Suppose we feed a learning algorithm a lot of historical weather data, and have it learn to predict weather. What would be a reasonable choice for P

Reasonable choice for P is the probability of it correctly predicting a future date's weather.

Explanation:

In Machine Learning, the computer or machine learns from experience  with respect to some task  and some performance measure. In this example the learning algorithm is fed to with a bulk of weather data with the goal to learn that data to be able to predict weather. So the task is to predict weather and performance measure is the probability of predicting the weather correctly. A learning algorithm can guess the weather correctly or incorrectly so as it keeps learning, it gains some experience and this experience improves its ability to perform the task. In this example the task of correctly predicting weather improves with experience. So its performance on task T of predicting weather, as measure by P which is the probability of correctly predicting future date's weather improves with experience E which is some function or procedure that it uses for weather prediction. Hence here performance measure P of this machine/program is the correct prediction of the weather of future date.