Let a discrete-time stochastic process {X 0 , X 1 , ...} be defined by where the random variables Y i are independent and have a uniform distribution over the interval [0, T]. Under which condition is...

Let a discrete-time stochastic process {X₀, X₁, ...} be defined by

where the random variables Y_i
are independent and have a uniform distribution over the interval [0, T]. Under which condition is {X₀, X₁, ...} (1) a martingale, (2) a sub-martingale, (3) a supermartingale?