Find the probability distribution of the maximum of two scores obtained when a die is thrown twice. Determine also the mean of the distribution.

Explanation

To solve the problem of finding the probability distribution of the maximum of two scores obtained when a die is thrown twice, and to determine the mean of that distribution, we can follow these steps:

### Step 1: Identify Possible Outcomes
When a die is thrown twice, the possible outcomes for each die are 1, 2, 3, 4, 5, and 6. Therefore, the total number of outcomes when throwing two dice is \(6 \times 6 = 36\).

### Step 2: Determine the Maximum Values
We need to find the probability distribution of the maximum score, which can take values from 1 to 6. We will calculate the probability for each maximum value.

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