Build robots that see, think & move.

Run a browser cell; use variables, lists, loops, functions and numpy arrays; read sums, averages, area under a curve and slope.

Define a sample space, an event and a probability measure from the axioms, and compute probabilities on finite spaces.

Describe a random variable with a PMF, PDF or CDF, and recognise the Bernoulli, binomial, uniform and exponential distributions.

Compute expectation, variance and covariance, and use linearity of expectation without assuming independence.

Work with conditional probability, the chain rule, independence and conditional independence.

Apply Bayes' rule, connect prior, likelihood and posterior, and classify with a maximum-a-posteriori decision.

Explain the law of large numbers and the central limit theorem, and reason about sampling distributions.

Use vectors in R^n, build linear combinations, and reason with the dot product and orthogonality.

Recognise linear maps, compute matrix-vector products and compose transformations.

Frame learning as empirical risk minimisation and follow a gradient-descent update from gradient to chain rule.

Describe the agent–environment loop, explain the reward hypothesis, and name the ingredients of a Markov decision process.

Compute discounted returns, explain value functions, and use the Bellman equation to relate a state's value to its successors.

Explain the exploration/exploitation trade-off and measure a bandit algorithm by its regret.

Run and compare two principled bandit algorithms: UCB1 and Thompson sampling.

Explain the sense-decide-act loop, name a robot's joints, links and end effector, and predict how a joint angle moves the hand.

Separate true state, prediction, measurement and estimate, and explain why combining a prediction with a measurement helps.