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The concept of the median of a set of data can also be applied to the...

  1. The concept of the median of a set of data can also be applied to the probability distribution of a random variable. If x is a random variable with density function f (x), then the median of this distribution is defined to be the value  for which half the area under the density curve lies to the left of . That is,

is the solution to the equation  .

  1. Suppose the lifetime x of an electronic assembly follows an exponential distribution with an

MTBF of 1000 hours (see Example 5.12 for the definition of MTBF). Find the median of this distribution. The median is the time by which half of all such assemblies will break down.

  1. Is the median time to failure from part (a) larger or smaller than the mean time before failure

(MTBF)?

  1. From your answer to part (a), find a general formula (for any value of MTBF) for expressing

the median time to failure in terms of the mean time before failure.

Math   Statistics-And-Probability   
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