Probability

Probability is the language in which returns and risk are expressed. Random variables model unknown payoffs; distributions such as the normal, lognormal, and Student t describe how returns behave, including their fat tails; expectation and variance summarize reward and dispersion; Bayes’ theorem updates beliefs as new prices arrive. These ideas drive everything from volatility estimation to derivative pricing, where an expectation under a risk-neutral measure defines fair value. Keep the discrete-to-continuous bridge in mind: coin flips and random walks converge toward Brownian motion, the object the quant core track builds on. A solid grasp here makes statistical inference feel like the natural next step.