This letter quantifies the effect of random model uncertainty on finite horizon linear time-varying (LTV) systems. Mean and standard deviation field are approximated with high accuracy and efficiency by a Hilbert space technique called polynomial chaos expansion (PCE). The deterministic expansion coefficients of the generalized Fourier series are determined via orthogonal projection, also known as Galerkin projection. We propose the projection of uncertain systems in linear fractional representation (LFR), which can have computational benefits. The technique is benchmarked on a two-link robotic manipulator.