The joint probability density function of independent random variables $X$ and $Y$ is $\frac{1}{34}$ on the region$0<x<6, 0<y<6, x+y<10.$ I am trying to find $E[X]$ however I am stuck at defining the limits of the integrals.
My approach is to find the marginal pdf for $X$ by: $$f_X(x)= \int_0^{10-x} \frac{1}{34} \ dy$$ then solve for $E[X]$ using: $$E[X]=\int_0^6 xf_X(x) \ dx$$

However I am doubting that my limits for both integrals are correct. Could anyone help me with this, please. Thank you.

  • 2
    $\begingroup$ Make a drawing. $\endgroup$ – Jarle Tufto Apr 1 at 13:29
  • $\begingroup$ There are two upper bounds on $y$. $\endgroup$ – Xi'an Apr 1 at 14:06