Mathematics, 05.07.2019 18:20, noriega16
Suppose x and y are random variables with joint density function. f(x, y) = 0.1eā(0.5x + 0.2y) if x ā„ 0, y ā„ 0 0 otherwise (a) is f a joint density function? yes no (b) find p(y ā„ 8). (round your answer to four decimal places.) find p(x ā¤ 5, y ā¤ 8). (round your answer to four decimal places.) (c) find the expected value of x. find the expected value of y.
Answers: 1
is a joint density function if its integral over the given support is 1:
:
, so we just integrate:![E[Y]=\displaystyle\int_{-\infty}^\infty y\,f_Y(y)\,\mathrm dy=\frac15\int_0^\infty ye^{-y/5}\,\mathrm dy=\boxed5](/tpl/images/0054/9757/d232b.png)
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Suppose x and y are random variables with joint density function. f(x, y) = 0.1eā(0.5x + 0.2y) if x...
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