A random variable X is exponentially distributed with an expected value of 50. a-1. What is...

A random variable X is exponentially distributed with an expected value of 50.

a-1. What is the rate parameter λ? (Round your answer to 3 decimal places.)

a-2. What is the standard deviation of X?

b. Compute P(44 ≤ X ≤ 56). (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.)

c. Compute P(36 ≤ X ≤ 64). (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.)

Solutions

Expert Solution

a-1

The parameter of an exponential distribution is given as

Where is the expected value

Hence

a-2

Standard deviation is the same as the expected value of X i.e. 50

a-3

We need to compute . Therefore, the following is obtained:

a-4

We need to compute Pr(36≤X≤64). Therefore, the following is obtained:

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orchestra answered 1 year ago

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