(Solved): A random variable \( X \) is exponentially distributed with an expected value of 60 . a-1. What is ...

A random variable \( X \) is exponentially distributed with an expected value of 60 . a-1. What is the rate parameter \( \lambda \) ? (Round your answer to 3 decimal places.) a-2. What is the standard deviation of \( X \) ? b. Compute \( P(50 \leq X \leq 70) \). (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.) c. Compute \( P(42 \leq X \leq 78 \) ). (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.)