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August 9th, 2017, 09:06 AM   #1
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Find the support of the density function of the random variable $X + Y$ .

The support of a function $f(x)$ is defined to be the set
$\{x : f(x) > 0\}$ .

Suppose that $X$ and $Y$ are two continuous random variables with density
functions $f_X(x)$ and $f_Y (y)$, respectively, and suppose that the supports of
these density functions are the intervals $[a, b]$ and $[c, d]$, respectively.

Find the
support of the density function of the random variable $X + Y$ .


Attempt: I tried to set up and take the integral $$\int_{0}^{z} (z-x)(x)\,\mathrm dx$$ and eventually ended getting $\frac{z^3}6$, however this doesnt seem to be right. How would u solve this?
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August 9th, 2017, 10:06 AM   #2
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The support of a continuous random variable is just the set of values that have non-zero probability.

It should be obvious at first glance that the support of $X + Y$ is just $[a+c, b+d]$

The bounds are just the minimum and maximum attainable values of $X+Y$
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August 10th, 2017, 09:08 AM   #3
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Is there a procedure or steps on how you got a+c and b+d, Romsek?
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