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(X²) = 1²(1/9) + 2²(3/9) + 3²(5/9) = 58/9

Therefore the variance now is computed here as:
Var(X) = E(X²) - [E(X)]² = (58/9) - (22/9)² = 38/81

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