Question

Let Y and Y have the joint probability density function given by for Find the marginal density of Y.

Answer 1

To find the marginal density of Y, we integrate the joint probability density function (PDF) with respect to X. In this case, the marginal density of Y is 2.

Step-by-step explanation:

To find the marginal density of Y, we need to integrate the joint probability density function (PDF) with respect to X. Let's denote the joint PDF as f(x, y). The marginal density of Y, denoted as f(y), can be found by integrating f(x, y) over all possible values of X.

In this case, the joint PDF is given by f(x, y) = 0.5x for 0 ≤ x ≤ 2 and 0 ≤ y ≤ 1. To find the marginal density of Y, we integrate f(x, y) with respect to X:

f(y) = ∫02 0.5x dx = [0.25x^2]02 = 2 - 0 = 2.