Problem 1. Let W(t), 0 g t S T, be a Wiener process. 1. Write the density function 19(33, t) of the random variable W(t) at time t. 2. The function p(:c,t) is the solution to the heat equation (2.4) With the initial condi tion (2.5). Find 02 and 9(513). Heat equation. The heat equation is the partial differential equation (9 02 (92 t : u 59 t 2.4 am) 2656\