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[Solution Library] The duration of telephone calls in certain city is measured by a random variable X with probability density f(x)=0.5e^-0.5x where x denotes

Question: The duration of telephone calls in certain city is measured by a random variable \(X\) with probability density

\[f(x)=0.5{{e}^{-0.5x}}\]

where \(x\) denotes the duration in minutes of a randomly selected call

  1. What percentage of the calls can be expected to last between 2 and 3 minutes?
  2. What percentage of the calls can be expected to last 2 minutes or less?
  3. What percentage of the calls can be expected to last more than 2 minutes

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