Determining the First Probability Density Function of Linear Random Initial Value Problems by the Random Variable Transformation (RVT) Technique: A Comprehensive Study

Figure 3

Plots of 𝑓₁(𝑧,𝑡) given by (54) in Example 12 at different values of 𝑡={0.1,0.2,0.3,…,1.5} (corresponding to the solid lines in both plots) in the case that (𝑍₀,𝐴) is a two-dimensional RV whose PDF is given by (52) and 𝑡₀=0.

(a)

(b)