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

Figure 6

Plot of 𝑓₁(𝑧,𝑡) given by (79)-(80) in Example 15 at different values of 𝑡={0,0.1,0.2,…,1.5} (corresponding to the solid lines in both plots) in the case that (𝑍₀,𝐵) is a two-dimensional RV whose PDF is given by (77) and 𝑡₀=0.

(a)

(b)