Let X denote the number of spots on a single throw of a fair 6-sided die. Find the mean, variance, and standard deviation of X. If you can, relate the mean and variance to the mean and variance.

 

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For the random variable T of the preceding example, find E(T) and E(T2). Solution: Extending the table of Example 1, 2 3 4 f(t) tf(t) 6. 8. 10 11 12 3 36 36 36. 12 36 36 T00 36 180 36 36 320 36 36 324 36 212 36 300 36 144 36 36 36 36 36 Adding the entries in the last two rows gives E(T) = 7 and E(T*) = 54.833. For the random variable T of the preceding example, find E(T) and E(T2). Solution: Extending the table of Example 1, 2 3 4 f(t) tf(t) 6. 8. 10 11 12 3 36 36 36. 12 36 36 T00 36 180 36 36 320 36 36 324 36 212 36 300 36 144 36 36 36 36 36 Adding the entries in the last two rows gives E(T) = 7 and E(T*) = 54.833.

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