# Limits of integrals for marginal pdf and expected values [duplicate]

The joint probability density function of independent random variables $$X$$ and $$Y$$ is $$\frac{1}{34}$$ on the region$$0 I am trying to find $$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.

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