# Consider two independent and identically distributed continuous uniform random variables, X U[0,3] and Y U[0,3] with densities (equal, and shown…

Consider two independent and identically distributed continuous uniform random variables, X∼ U[0,3] and Y∼ U[0,3] with densities (equal, and shown twice for convenience). fX(x) ={ c = 1 3 for 0 ≤ x ≤ 3 0 otherwise fY (y) ={ c = 1 3 for 0 ≤ y ≤ 3 0 otherwise

(a) (5 points) Derive the density g(t) for the sum of the random variables, T = X + Y . (b) (5 points) Draw the (x,y)-plane where X and Y are deﬁned and non-zero, and indicate the range of values where T might be deﬁned diﬀerently. Make sure you include the range of values where the density of T is zero(0).(please provide process)

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