An oscillator sends the wave X(t) = A cos(2t), where A = 1 or 2 with equal probabilities. We observe the value of X(t) at

An oscillator sends the wave X(t) = A cos(2πt), where A = 1 or 2 with equal probabilities. We observe the value of X(t) at the point chosen at random from the U[n,n + 1] distribution for some n. Find: (i) P(X(t) ≤ 1). (ii) P(|X(t)| > 3/2).

(iii) P(X(t) > 0).