A convenience store has two separate locations where customers can be checked out as they leave. These locations each have two cash registers and two employees who check out customers. Let X be the number of cash registers being used at a particular time for location 1 and Y the number being used at the same time for location 2. The joint probability function is given by the accompanying table. Complete parts (a) through (c) below. Click the icon to view the joint probability function. (a) Give the marginal density of both X and Y as well as the probability distribution of X given Y = 2. Let g(x) be the marginal density of X and let h(y) be the marginal density of Y. Give the marginal density of both X and Y. X g(x) y h(y) 2 2 (Type integers or decimals. Do not round.)

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