Core sequence
Build from discrete expected value into linearity, indicator variables, geometric waiting times, repeated games, conditional EV and optimal stopping.
Linearity does not require independence. This single fact shortens many interview problems dramatically.
Fastest useful method
List outcomes only when the state space is small. For counts, define an indicator for each possible contribution. For repeated trials, identify whether the remaining problem resets after a miss.
Trading application
Fair value is an expected payoff under a stated information set. A good quote must also account for uncertainty, inventory and what an incoming trade may reveal.
Practice the central quant branch.
Fresh EV questions range from one-roll games to waiting times and stopping decisions.
Train expected value