Using the Bayes' Net and conditional probability tables above, calculate the following quantities: (i) P(+a,+b) = (ii) P(+al+b) = (iii) P(+al-b) = %3!

X is a discrete random variable with the following PMF: P(X = 1.4) = 0.25 P(X = -9.7) = 0.25 P(X = 10) = 0.5 Find the standard deviation of X.

The would not be viewed as having a probability distribution? deterministic factors input factors output variables simulation method

2. Take a bivariate normal distribution with two random variables X and Y, with mean value = (1, -1), var(X) = 3, var(Y) = 6, and cor(X,Y) = -0.5. %3! (a) create a contour plot for this data (b) plot 1,000 simulations of this distribution (c) Using 1,000,000 simulations, find (1) the expected value of Y (ii) the expected value of Y, given that X> 2 (ii) the expected value of Y, given that X = 2

Consider the graph of a Bayesian Network shown below showing 7 binary random variables. Age Gender Exposure to Toxics Serum Calcium Cancer Smoking Lung tumor How many probabilities will be needed to complete the conditional probability table of variable "Cancer"? How many probabilities will be needed to complete the conditional probability table of variable "Lung tumor"? How many probabilities will be needed in total to complete all the conditional probability tables of this BN? How many probabilities will be needed to complete the joint probability table of all variables? Give the answers for each question as a number (e.g., 4)

Explain how we perform maximum likelihood

For each of the attached probabilistic expressions, please answer "yes" or "no" to indicate if it is equal to P(A,B,C), given Boolean random variables A, B and C , and no independence or conditional independence are assumed between any of them.