Find the expected value for the random variable of an unbiased die.

Answer»

Let X denote the number on the top side of the unbiased die.

The probability mass function is given by the following table.

X = x	1	2	3	4	5	6
P(x)	1/6	1/6	1/6	1/6	1/6	1/6

The expected value for the random variable X is

E(X) = ∑_xxP_x(x)

= (1 x 1/6) + (2 x 1/6) + (3 x 1/6) + (4 x 1/6) + (5 x 1/6) + (6 x 1/6)

= 1/6(1 + 2 + 3 + 4 + 5 + 6)

= 21/6 = 7/2 = 3.5

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