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'S' is the sample space obtained when a pair of symmetric dice are tossed, X is the random variable defined by X(a, b) = max $\{a, b\}$ so that the range of X is the set
$\{1, 2, 3, 4, 5, 6\}$ . Then, the mean of X is

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4.47

4.97

5.5

5.57

answer is D.

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Detailed Solution

Given X is random Variable defined by $X (a, b) = \max {a, b}$

X	1	2	3	4	5	6
P(X=x)	$\frac{1}{36}$	$\frac{3}{36}$	$\frac{5}{36}$	$\frac{7}{36}$	$\frac{9}{36}$	$\frac{11}{36}$

Mean $(μ) = \sum x P (X = x)$

$= 1 (\frac{1}{36}) + 2 (\frac{3}{36}) + 3 (\frac{5}{36}) + 4 (\frac{7}{36}) + 5 (\frac{9}{36}) + 6 (\frac{11}{36}) = \frac{1 + 6 + 15 + 28 + 45 + 66}{36} = \frac{161}{36} = 4.47$

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