2 3. (10 pts) A discrete choice model of travel mode to work includes two alternatives: driving alone (alternative 1) and taking transit (alternative 2). The model is based on the following utility functions: U₁= 1- t + ₁ U2 = 42- t^+ 2 Probability and Discrete Choice Models where 1 and 2 are model parameters. Both error terms 1 and 2 follow a uniform distribution between -b and b. (a) Develop an analytical expression for P₁ as a function of 9₁, 92, t, t^, and b. (b) Assume that 41 - 92= 1 and plot P₁ versus t^-t for several values of b. Discuss the effect of b on the choice probability and draw general conclusions.

Fig: 1