Question: The random variable Y is the sum of the dice when two balanced dice are rolled. Its probability distribution is as follows. For each exercise,

The random variable Y is the sum of the dice when two balanced dice are rolled. Its probability distribution is as follows.

For each exercise, do the following tasks.

a. Find and interpret the mean of the random variable.

b. Obtain the standard deviation of the random variable by using one of the formulas given in Definition 5.10.

c. Construct a probability histogram for the random variable; locate the mean; and show one-, two-, and three-standard-deviation intervals.

2 1 P(Y =y) | 36 y 3 1 18 4 12

Definition 5.10

The standard deviation of a discrete random variable X is denoted σX or, when no confusion will arise, simply σ. It is defined as 5 6 5 36 789 6 5 36 10 11 12 12

The standard deviation of a discrete random variable can also be obtained from the computing formula 18 1 36

2 1 P(Y =y) | 36 y 3 1 18 4 12 5 6 5 36 789 6 5 36 10 11 12 12 18 1 36

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