6. A dart is thrown at a dartboard with concentric circles. If the radius of the

Question

6. A dart is thrown at a dartboard with concentric circles. If the radius of the circle is a Rayleigh variable with a parameter 0.5, what is the probability that the dart thrown lands in a disc of thickness 0.2 units with the center at 1 unit. A call center receives telephone calls with an average duration of 3 minutes. What is the probability that the next call received will exceed the average duration given that calls generally last longer than 2 minutes. (Call duration is exponentially distributed). 7.

Explanation / Answer

Please post 1 question per post as per forum rules. Here' answer to the question 7.Write back to me in case you don't understand anypart of it

The cumulative probabilty is given by ; CDF = 1- e^(-Lambda*x)

Therefore, lets define the params of the disrtibution according to the infomration given in the question:

Lambda = 3 =5minutes, x = 2+3 minutes = 5 minutes

The probability that next call received will exceed the average duration given that calls genrally last longer than 2 mins  

= 1- e^(-5*3) = .999

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