Final answer:
The correlation coefficient between the given signals can be calculated using a formula, and its value can indicate the strength and direction of the relationship between the signals. The significance of the decrease in times depends on the calculated correlation coefficient.
Step-by-step explanation:
The correlation coefficient between the signal g1(t) = u(t) - u(t - 2) and the signal g2(t) = exp(-0.5t) u(t) can be found using the formula for correlation coefficient:
r = (Σ(g1_i - mean(g1))(g2_i - mean(g2)))/(sqrt(Σ(g1_i - mean(g1))²) sqrt(Σ(g2_i - mean(g2))²))
Once you calculate the correlation coefficient, you can interpret its value to determine the strength and direction of the relationship between the two signals. The decrease in times would be considered significant if the correlation coefficient is significantly different from 0.