27 May, 02:08

# The following table shows the probability of rolling the numbers 1 through 7 on a fair seven-sided die.X 1 2 3 4 5 6 7P (X) 1/7 1/7 1/7 1/7 1/7 1/7 1/7What is the standard deviation of the random variable X, "the number that comes up on the die?"

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Answers (1)
1. 27 May, 02:51
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E (X) = 1/7 + 2 (1/7) + 3 (1/7) + 4 (1/7) + 5 (1/7) + 6 (1/7) + 7 (1/7) = 1/7 + 2/7 + 3/7 + 4/7 + 5/7 + 6/7 + 7/7 = 24/7 = 4.

Var (X) = 1/7 (1 - 4) ^2 + 1/7 (2 - 4) ^2 + 1/7 (3 - 4) ^2 + 1/7 (4 - 4) ^2 + 1/7 (5 - 4) ^2 + 1/7 (6 - 4) ^2 + 1/7 (7 - 4) ^2 = 9 (1/7) + 4 (1/7) + 1/7 + 1/7 + 4 (1/7) + 9 (1/7) = 9/7 + 4/7 + 2/7 + 4/7 + 9/7 = 28/7 = 4

standard deviation = sqrt (Var (X)) = sqrt (4) = 2.
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