Homework Handout #1

1) What are the relative and absolute precisions implied by the following three numbers:

• 5

• 42

• 6.66x10²

2) What is the probability of getting at least 4 cosmic rays in a two second window if the average rate is 1.69 per 2 seconds? Work the infinite series out by hand, until it converges to 3 significant digits, or find a clever work-around (by hand. Computers aren't clever). For problems #3 & #4, you don't have to be explicit with the series, you can have a machine calculate it for you if the arithmetic is too nasty (just tell me what you did).

3) A more relevant question to part of my job (Bevington, problem 2.9):

In a certain physics course, 7.3% of the students failed and 92.7% passed, averaged over many semesters. If this semester there are 32 students,

• What is the expected number of failures?

• What is the probability that 5 or more students will fail?

4) And lastly, a very relevant question to the other part of my job (Bevington, prob. 2.13):

Members of a large collaboration that operates a giant proton decay detector in a salt mine near Cleveland, Ohio, detected a burst of 8 neutrinos in their apparatus coincident with the optical observation if the Supernova 1987A.

• If the average number of neutrinos detected in the apparatus is 2 per day, what is the probability of detecting a fluctuation of 8 or more in one day?

• In fact, the 8 neutrinos were all detected within a 10-min period. What is the probability of detecting a fluctuation of 8 or more neutrinos in a 10-min period if the average rate is 2 per 24 hours?