Homework for Spins

  1. (DieOne) This problem asks several questions that are also pertinent to the Rolling Dice Lab, and involves several general probability calculations.

    A classical cubical die is thrown onto a table and comes to rest, where a measurement is made of its state.

    1. What are the possible results of this measurement?

    2. What are the predicted probabilities for these possible outcomes?

    3. Plot a histogram of the predicted meaurement results.

    4. Suppose you roll the die 12 times. What is the theoretical probability that you the number 1 will be face up precisely four times? Plot a histogram that the number 1 will be face up precisely $n$ times. How is this histogram different from your histogram from part $(c)$?

    5. Find the theoretical mean and standard deviation for obtaining $n$ observations of the number 1 if you make twelve independent measurements. Repeat for 120 independent measurements.

    6. Suppose you roll the die 12 times and get the number 1 4 times. How sure are you that the die is fair? Suppose you roll the die 120 times and get the number 1 40 times. How sure are you that the die is fair?


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