Consider the Bayesian Network below. A D C Q B E How many probabilities will be needed in total to complete all the conditional probability tables of this BN?

We consider a Bayesian network with 74 variables including Variables A, B, and C. If we want to study inference P(A|B,C), how many hidden variables are there?

A confusion matrix based on one particular cut-off probability can determine the entire ROC curve.     True     False

The following MDP world consists of 5 states and 3 actions: (1, 1) (1, 2) Action: Exit - -10 Actions: down, right (2, 1) (2, 2) Action: Exit = -10 Actions: down, right (3, 1) Action: Exit = 10 When taking action down, it is successful with probability 0.7. with probability 0.2 you go right, and with probability 0.1 you stay in place. When taking action right, it is successful with probability 0.7, with probability 0.2 you go right, and with probability O.1 you stay in place. When taking action Exit, it is successful with probability 1.0. The only reward is when taking action Exit, and there is no discounting. Calculate the value of states using Value Iteration algorithm for required time step: Provide the value for State (1,2) at time step 4 (calculate to 3 decimal places): Va(1,2) =

t-SNE tries to minimize the divergence between the probability distributions of neighbors in original space and in reduced space.  From this case, is it True or False?

show that the MLE for this model also minimizes the sum of absolute errors (SAE): Note that you do not need to solve for an expression for the actual MLE expression for w to do this problem. Simply showing that the likelihood is proportional to SAE is sufficient.

How many? Consider a probability experiment in which the sample space is S = {1,2} How many events are there in this probability experiment? {1}{2}{1,2}

In the theoretical landscape of probability theory, a multifaceted inquiry unfolds: Can we dissect the complexities of stochastic processes and their role in modeling dynamic systems over time? How do concepts like Markov chains and Brownian motion contribute to understanding the evolution of random phenomena, transcending mere chance into a nuanced exploration of theoretical probabilities with real-world implications? Furthermore, how does the convergence of these theoretical frameworks amplify our ability to analyze and predict the uncertain trajectories of diverse phenomena in fields ranging from finance to physics?

For the Covid-19 pandemic, let’s make the following assumptions: (i) the natural infection rate is 20% (i.e., a person who is not vaccinated has 20% chance of being infected); (ii) the vaccine is 90% effective at preventing Covid-19 infection (i.e., a vaccinated person has only 2% chance of being infected); (iii) the probability of a random person being vaccinated is 60%. Without knowing whether or not a person is vaccinated, what is the probability that this person will be infected? Given that a person is infected, what is the conditional probability that this person is vaccinated?

Probability Consider a probability experiment with S = {0, 1, 2, 3, 4, 5, 6, 7} and these two events: A = {1,2, 3}, and B= {1,3, 5, 6, 7} What is the probability that A occurs? What is the probability that B occurs? What is the obability that A n B occurs? What is the probability that AU Boccurs? What is the probability that {} occurs? What is the probability that S occurs?