$X = Binom(5,0.5)$ and $Y=U(0,1)$. we need to find $P(X+Y \geq2)$
using characteristic function. This is what I could solve but could not go ahead.
$C_X(t)=\frac{(e^{it}+1)^5}{2^5}$
$C_Y(t)=\frac{e^{it}-1}{it}$
Taking $Z=X+Y$ and since both X and Y are independent.
$C_Z(t)=C_X(t)C_Y(t)= \frac{(e^{it}+1)^5(e^{it}-1)}{2^5\cdot it}$
After this what should I do, integration would not be feasible.