(ii) Let X and Y have joint density $f(x, y) = \begin{cases} \frac{6}{5}(x + y^2), & \text{for } 0 \le x \le 1; 0 \le y \le 1\\ 0, & \text{otherwise} \end{cases}$ Find the $P(0 \le X \le \frac{1}{4}, 0 \le Y \le \frac{1}{4})$
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To find the marginal density function of X, we integrate the joint density function over the range of Y: f_X(x) = ∫[0,1] f(x,y) dy = ∫[0,1] 1/v dy = 1/v * y |[0,1] = 1/v Similarly, to find the marginal density function of Y, we integrate Show more…
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