The article "A model of Pedestrian Waiting Times for Street Crossings at Signalized Intersections" (Transportation Research, 2013) suggested that under some circumstances the distribution of waiting time X could be modeled with the following pdf: f(x;θ,τ) = (θ/τ)(1-x/τ)θ-1, for 0 <= x < r f(x;θ,τ) = 0, otherwise
1. Obtain an expression for the 25-th percentile of the waiting time distribution, in function of parameters θ and τ.
2. For the case θ = 1 and τ = 110, calculate P(40 < X < 70)