Task 2: Distribution of a total score
Task 2: Distribution of a total score
Suppose we roll two dice at a time and record the sum Y = X1 + X2 of the observed values X1 and X2.
- The possible values of the sum Y are in the range from 2 to 12. Which of those do you think are most likely to be observed? Why?
- Confirm your intuition by simulating sequences of rolls of two dice and noting a sample mode of the simulated values of Y.
- Create a bar plot to visualise the frequency distribution of possible values of Y. Does it look like a ‘normal’ plot? Does the normal approximation improve with the growth of the number of trials?
- Design and carry out a simulation to evaluate numerically the probability P(Y = 7).
- Calculate the MOE of your estimation. What prediction can you make about the exact value of the probability P(Y = 7)?
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