Question

When a ray arrives at my sensor, then it goes Ping!!. The average time between Ping!!s...

When a ray arrives at my sensor, then it goes Ping!!. The average time between Ping!!s is 2 minute and the appearance of rays follows a Poisson process.

a) What is the probability that the time between Ping!!s exceeds 1 minute

b) If two Ping!!s occur within 3 minutes of each other, what is the probability that none of the Ping!!s occurred in the middle minute (that is, after the first minute and before the last minute)?

Math   Statistics-And-Probability   
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Answer #1

a) The mean waiting time between the rays appearances here is given as 2 minute. The probability that the waiting time exceed 1 minute is computed here as:

Therefore 0.6065 is the required probability here.

b) The exponential distribution follows memoryless property, therefore the probability that none of the Ping!!s occurred in the middle minute is computed by not taking into account what happens in the other two minutes. Therefore the probability here is computed as:

Therefore 0.6065 is the required probability here.

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