Stats Solutions

(Step-by-Step) The useful life of a particular type of printer is measured by a random variable X with probability density: f(x)= 0.02e^-0.02x x≥ 0 , 0 x<0

Question: The useful life of a particular type of printer is measured by a random variable X with probability density:

\[f\left( x \right)=\left\{ \begin{aligned} & 0.02{{e}^{-0.02x}}\,\,\,\,\,x\ge 0 \\ & 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x<0 \\ \end{aligned} \right.\]

where x represents the number of months in use.

  1. What is the probability that a randomly selected printer will last between 10 and 15 months?
  2. What is the probability that a randomly selected printer will last less than 8 months?
  3. What is the probability that a randomly selected printer will last longer that 1 year?
  4. What is the expected life of a randomly selected printer?

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