2 3 10 pts a discrete choice model of travel mode to work includes two
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^+
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.
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