Find the median of an exponential random variable with

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QUESTION:

Find the median of an exponential random variable with rate . Recall that for a continuous distribution F, the median Q0.5 is the point at which F (Q0.5) = 1/2.

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QUESTION:

Find the median of an exponential random variable with rate . Recall that for a continuous distribution F, the median Q0.5 is the point at which F (Q0.5) = 1/2.

ANSWER:

Step 1 of 3

We are going to use following claim:

 If random variable  has exponential distributed with parametar , then the cumulative distribution function is .

Now, let's work out our problem:

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