QUESTION 5 Consider discrete random variables X and Y with possible values of 0 and 1 only for each. The joint p.m.f. values are as follows: . f(0,0) = 0.1, . f(0, 1) = 0.2, . f(1,0) = 0.4, . f(1,1) = ???, . f(x,y) = 0.0 otherwise. What is the value of f(1, 1) to make f(x,y) a valid joint p.m.f.? QUESTION 6 Which of the following is NOT TRUE about marginal distributions? O Marginal distribution g(x) for discrete random variable X is found by summing the joint distribution f(x,y) over all y-values. Similarly, marginal distribution h(y) for discrete random variable Y is found by summing the joint distribution f(x,y) over all x-values. Marginal distribution g(x) for continuous random variable X is found by integrating the joint distribution f(x,y) over the entire y-axis. Similarly, marginal distribution h(y) for continuous random variable Y is found by integrating the joint distribution f(x,y) over the entire x-axis. O Marginal distributions g(x) and h(y) have the same properties as a single variable probability distribution f(x) first introduced in Module 4. O Marginal distribution g(x) for discrete random variable X is found by summing the joint distribution f(x,y) over all x-values. Similarly, marginal distribution h(y) for discrete random variable Y is found by summing the joint distribution f(x,y) over all y-values. QUESTION 7 Which of the following is NOT TRUE about conditional distributions? A conditional distribution is the random variable extension of conditional probability for events from Module 3, since both defintions represent joint probability of both divided by total probability of the given. A conditional distribution is defined as the joint probability distribution divided by the marginal distribution for the random variable being conditioned (i.e. has a known value). The definition of conditional probability is different for discrete and continuous random variables. A conditional distribution can be integrated or summed to find the probability of one random variable taking on values in a specific interval when another random variable has a known value