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August 9th, 2017, 10:06 AM  #1 
Member Joined: Apr 2017 From: PA Posts: 45 Thanks: 0  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 $$\int_{0}^{z} (zx)(x)\,\mathrm dx$$ and eventually ended getting $\frac{z^3}6$, however this doesnt seem to be right. How would u solve this? 
August 9th, 2017, 11:06 AM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 1,763 Thanks: 905 
The support of a continuous random variable is just the set of values that have nonzero 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 $X+Y$ 
August 10th, 2017, 10:08 AM  #3 
Member Joined: Apr 2017 From: PA Posts: 45 Thanks: 0 
Is there a procedure or steps on how you got a+c and b+d, Romsek?


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density, find, function, random, support, variable 
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