Re: exponential R.V

The question is as follows

The durations of calls to a radio talk show are known
to be
exponentially distributed with a mean of 3 minutes.
Q1. Given that a call has already lasted 4 minutes,
what is the
probability that it will last at leat another 4
minutes?
Q2. Given that a call has already lasted 4 minutes,
what is the
expected remaining time until it ends?

So I'm going to solve these problems like this.

A1 to Q1) P[ X > 8 | X > 4]
A2 to Q2) E[ X | X > 4 }

Am I going to right way?



For an exponential, the conditional probability that X>t2, given that X>t1, is the unconditional probability that X>t2-t1. Thus,

Q1): exp(-4/3)

Q2): 4+E(X) = 4+3 = 7.

Jack
.

Relevant Pages

  • Re: Exponential R.V.
    ... The durations of calls to a radio talk show are known to be ... probability that it will last at leat another 4 minutes? ...
    (sci.math)
  • Re: Exponential R.V.
    ... dondora writes: ... The durations of calls to a radio talk show are known to be ... But use the "lack of memory" property to calculate this. ...
    (sci.math)