Let the variable be
Yc = theta_1 + theta_1*theta_2+ theta_1*theta_2 theta_3 + ....
where theta_i are i.i.d uniform random variables (i = 1,2,...) having
CDF such that F(x) = 0, x <=0. F(x) = x,
F(x) = 0<x<c and
F(x) = 1 , for x >=c.
1)for what values of c > 0 is E(Yc) finite.
2)Also, for what value of c > 0, Yc (sum converges with probability 1).