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- set.seed(1234) # for reproducibility
- B = 10^6; th = 6
- x1 = runif(B, 0, th); x2 = runif(B, 0, th)
- m = pmax(x1, x2); t2 = 1.5*m
- mean(m); mean(t2); var(t2)
- [1] 4.000053 # aprx E(M) = 4
- [1] 6.000079 # aprx E(T2) = 6 (unbiased)
- [1] 4.506313 # aprx Var(T2) < Var(T1)
- t1 = x1 + x2
- mean(x1); mean(t1); var(t1)
- [1] 2.998866 # a[rx E(X1) = 3
- [1] 5.998 # a[rx E(T1) = 6
- [1] 5.999963 # a[rx Var(T1) = 2(36)/12 = 6 > Var(T2)
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