A startup business school cafe tracks the number of premium coffees a randomly chosen customer buys in one visit. The random variable XXX denotes this number. Based on past data, the probability mass function of X is:  P(X=x)={0.1,x=0(no premium coffee),0.2,x=1(one premium coffee),0.3,x=2(two premium coffees),0.4,x=3(three premium coffees),0,otherwise.P(X=x) = \begin{cases} 0.1, & x=0 \quad (\text{no premium coffee}), \\ 0.2, & x=1 \quad (\text{one premium coffee}), \\ 0.3, & x=2 \quad (\text{two premium coffees}), \\ 0.4, & x=3 \quad (\text{three premium coffees}), \\ 0, & \text{otherwise}. \end{cases}

Using ________________________________________ approach, probabilities can only come from experiments.

The figure below shows two overlapping probability distributions: The left distribution (I) corresponds to impostor attempts, the right distribution (A) corresponds to authentic users, and a decision threshold is used to decide whether to accept or reject a person. Four possible outcomes exist depending on which side of the threshold the sample falls (A-D each letter is marked in a distinct region of the figure). Match each outcome below with the correct region: False Positive (Type II Error) (5 points) Correct Rejection (True Negative) (5 points) False Negative (Type I Error) (5 points) Correct Acceptance (True Positive) (5 points)

In the two-category case, if the class-conditional densities are Gaussian and the covariance matrix for each class is arbitrary, the decision surfaces are __________________________________________ (5 points).

An experiment whose result is not certain in advance is _______________________________________________________.

In the sense used by Clark, balance of power theory says that great powers will inevitably

Neo-realism

In statistical parameter estimation, _________________________________________ methods nearly always have good convergence properties as the number of training samples increases.

Which of the following is NOT a level of analysis addressed in this course?

Charles Lockhart is best associated with the argument that