### Joint Probability Density Function ProblemThe joint probability density function of the random variables $ X $, $ Y $, and $ Z $ is given by:\[f(x, y, z) = \begin{cases} \frac{1}{5} xyz^2, & 0 < x, y < 1, \ 0 < z < 3, \\0, & \text{elsewhere.} \end{cases}\]#### TasksFind:(a) The joint marginal density function of $ X $ and $ Y $.(b) The marginal density of $ Z $.(c) $ P\left(\frac{1}{7} < X < \frac{1}{2}, \, Y > \frac{1}{3}, \, 2 < Z < 3\right) $.(d) $ P\left(0 < Z < 2 \, | \, X = \frac{1}{2}, \, Y = \frac{1}{3}\right) $.

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Answered: 3.60 The joint probability density…

A First Course in Probability (10th Edition)

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3.60 The joint probability density function of the ran- dom variables X, Y, and Z is ry:", 0 }, 2 < Z < 3);: (d) P(0 < Z < 2 | X = }, Y = }).