Please see Lecture 2 for the definition of probability density function. The notion of transfer functions arise in describing behavior of linear time invariant dynamical systems in the Fourier or the Laplace domains. You will encounter these notions later in Lectures 10-17 for sdof, discrete mdof and continuous systems. There is no conceptual relation between the notions of probability density function of a random variable and transfer function of a dynamical system.
I could be of further assistance to you if you could clarify the origins of your doubt.
Prof. C.S. Manohar Date: