Explanation Given information: The time elapsed between successive resignations is an exponential random variable with expected value 2 years, that is E ( X ) = 2 . Explanation: Let X be a random variable which denotes time elapsed between successive resignations. Since X is an exponential random variable, its density function is f ( x ) = k e − k x ; x ≥ 0 , for some k > 0 and E ( X ) = 1 k . Given expected value is E ( X ) = 2 . Compare E ( X ) = 1 k with E ( X ) = 2 . This indicates 1 k = 2 . ⇒ k = 1 2 And therefore, density function f ( x ) = k e − k x becomes f ( x ) = 1 2 e − ( 1 / 2 ) x ; x ≥ 0 . Use theformula below tofind Pr ( X < 4 )

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Chapter 12.4, Problem 11E

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The probability that the next vacancy on the court will take place during the president’s 4-year term, that is, find Pr(X<4), where the time elapsed between successive resignations is an exponential random variable with expected value 2 years.

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Chapter 12.4, Problem 10E

Chapter 12.4, Problem 12E

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The probability that the next vacancy on the court will take place during the president’s 4 -year term, that is, find Pr ( X < 4 ) , where the time elapsed between successive resignations is an exponential random variable with expected value 2 years.

Solution Summary: The author analyzes the probability that the next vacancy on the court will take place during the president's 4 -year term.

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The probability that the next vacancy on the court will take place during the president’s 4-year term, that is, find Pr(X<4), where the time elapsed between successive resignations is an exponential random variable with expected value 2 years.

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Chapter 12 Solutions

The probability that the next vacancy on the court will take place during the president’s 4 -year term, that is, find Pr ( X &lt; 4 ) , where the time elapsed between successive resignations is an exponential random variable with expected value 2 years.

Solution Summary: The author analyzes the probability that the next vacancy on the court will take place during the president's 4 -year term.

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The probability that the next vacancy on the court will take place during the president’s 4-year term, that is, find Pr(X<4), where the time elapsed between successive resignations is an exponential random variable with expected value 2 years.

Want to see the full answer?

Chapter 12 Solutions

The probability that the next vacancy on the court will take place during the president’s 4 -year term, that is, find Pr ( X < 4 ) , where the time elapsed between successive resignations is an exponential random variable with expected value 2 years.