Final answer:
To determine the marginal density function of Y from the given joint probability density function of X and Y, integrate the joint function over the range of X. The area under the marginal density function graph represents the probability. An exact function for g(y) requires the full definition of xy(x, y).
Step-by-step explanation:
The question is asking for the marginal density function of Y, given a joint probability density function of two continuous random variables, X and Y. To find the marginal density function of Y, denoted as g(y), we need to integrate the joint probability density function with respect to x over the range of x for which the function is defined. In this case, the joint density function is partially defined but implies that it depends on x and is defined for x less than or equal to y. Thus, to get g(y), we integrate the joint pdf xy(x, y) with respect to x from negative infinity to y.
We use the probability density function (pdf) concept which indicates that the area under the pdf graph equals the probability. Since the total area under a pdf must equal one, according to the properties of probability distributions, marginalizing the joint pdf over x will give us the marginal pdf of Y.
Note, however, that to provide the exact function g(y), the joint density function xy(x, y) must be fully defined. Since it isn't provided here, the student would be expected to perform the integration with the actual xy(x, y) function, if known.