Let c 0 and 0 1 Also let X, Y, and T be random variables a If P(X c) , determine P(X c) in terms of b If P(Y c) 2 and P(Y c) P(Y c), obtain P(c Y c) in terms of c Suppose that P(c T c) 1 and, moreover, that P(T c) P(T c) Find P(T c) in terms of ...

a PX c PX c 1 Since PX c PX c 1 or PX c 1 b PY c Pc Y c PY ...

Let c > 0 and 0 1. Also let X, Y, and T be

Question:

Let c > 0 and 0 ≤ α ≤ 1. Also let X, Y, and T be random variables.
a. If P(X > c) = α, determine P(X ≤ c) in terms of α.
b. If P(Y > c) = α/2 and P(Y < −c) = P(Y > c), obtain P(−c ≤ Y ≤ c) in terms of α.
c. Suppose that P(−c ≤ T ≤ c) = 1 − α and, moreover, that P(T < −c) = P(T > c). Find P(T > c) in terms of α.