Fig. 1. The domain of (U_n−1,W_n) for c1 with positive correlation.

Fig. 2. The domain of (U_n−1,U_n): (a) c1 with positive correlation; (b) c<1 with positive correlation; (c) c1 with negative correlation; (d) c<1 with negative correlation.

Fig. 3. The joint pdf of (U_n−1,U_n): (a) c=1.5 with positive correlation; (b) c=0.5 with positive correlation; (c) c=1.5 with negative correlation; (d) c=0.5 with negative correlation.

Fig. 4. The scatter diagram of (U_n−1,U_n), based on 10,000 pairs of observations: (a) c=1.5 with positive correlation; (b) c=0.5 with positive correlation; (c) c=1.5 with negative correlation; (d) c=0.5 with negative correlation.

Fig. 5. The joint pdf of (Y_n−1,Y_n) with μ=1: (a) c=1.5 with positive correlation; (b) c=0.5 with positive correlation; (c) c=1.5 with negative correlation; (d) c=0.5 with negative correlation.

Fig. 6. The scatter diagram of (Y_n−1,Y_n) with μ=1, based on 10,000 pairs of observations: (a) c=1.5 with positive correlation; (b) c=0.5 with positive correlation; (c) c=1.5 with negative correlation; (d) c=0.5 with negative correlation.

Table 1. The exact value of ρ(c) for correlated uniform random variables

Table 2. Numerical values of ρ(c) for correlated exponential random variables

Table 3. Numerical values of ρ(c,p) for positively correlated Bernoulli random variables

Table 4. Numerical values of ρ(c,p) for negatively correlated Bernoulli random variables

LB denotes the lower bound.

Table 5. Numerical values of ρ(c,p) for positively correlated geometric random variables

Table 6. Numerical values of ρ(c,p) for negatively correlated geometric random variables

LB denotes the lower bound.