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

Figure 13

Plot of 𝑓₁(𝑧,𝑡) given by (152) in Example 23 at different values of 𝑡={0.1,0.2,…,1} (a) and 𝑡={1,1.1,…,2} (b) in the case that 𝑧₀=0 and 𝑡₀=0 and the joint PDF of (𝐵,𝐴) is given by (150). In order to better highlight the shape of 𝑓₁(𝑧,𝑡), we have split its representation into two plots. Notice the different scales in the vertical axes for each plot.

(a)

(b)