Question

Two
three partitioned spinners are spun. Each of the three parts have
an equally likelihood occuring. Let X be the maximum of two spins.
Find Var(X).

Answer #1

The PDF for X here is obtained as:

P(X = 1) = P(both get a 1) = (1/3)*(1/3) = 1/9

P(X = 2) = P(12, 21, 22) = 3/9

P(X = 3) = P(31, 32, 13, 23, 33) = 5/9

Therefore the expected value and second moment of X now are computed here as:

E(X) = 1*(1/9) + 2*(3/9) + 3*(5/9) = 22/9

E(X^{2}) = 1^{2}(1/9) + 2^{2}(3/9) +
3^{2}(5/9) = 58/9

Therefore the variance now is computed here as:

Var(X) = E(X^{2}) - [E(X)]^{2} = (58/9) -
(22/9)^{2} = 38/81

**Therefore 38/81 = 0.4691 is the required variance
here.**

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