Question-94

If \(X \sim \text{Exp}(\lambda)\), then find the value of \(P(X \leq 2+x \hspace{0.5mm} | \hspace{0.5mm} X \geq 2)\).

• \(P(X \leq 2)\) .

• \(P(X \leq x)\) .

• \(P(X > 2)\).

• \(P(X > x)\) .

NoteHint

Use memoryless property or use the conditional probability formulas as \(P( A ~ | ~ B) = \dfrac{P(A \cap B)}{P(B)}\)

NoteAnswer

• \(P(X \leq 2)\) .

• \(P(X \leq x)\) .

• \(P(X > 2)\).

• \(P(X > x)\) .

NoteSolution