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

Figure 10

Plot of 𝑓₁(𝑧,𝑡) given by (96) in Example 20 at different values of 𝑡={0,0.1,0.2,…,1} (a) and 𝑡={0.9,1,1.1,…,2} (b) in the case that 𝐴∼Be(2;3), 𝑡₀=0, 𝑧₀=1, and 𝑏=1. In order to highlight better 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)