Question

Two three partitioned spinners are spun. Each of the three parts have an equally likelihood occuring....

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).

Homework Answers

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.

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