# 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.

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.

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