It\'s ok if you provide solution to only one of them. 5. Messages arrive at a te

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It's ok if you provide solution to only one of them.

5. Messages arrive at a telegraph office in accordance with the laws of a Poisson (a) What is the probability that no message will have arrived during the (b) What is the distribution of the time at which the first afternoon message 6. Let, X(t) be a homogeneous Poisson process with parameter ?. Determine process with mean rate of 3 messages per hour morning hours (8 to 12)? arrives? the covariance between x(1) and X(t+t), t>0 and ?> 0, i.e., compute

Explanation / Answer

Question 5

Here expected number of calls to be arrived during the morning hours = 4 * 3 = 12 messages per hour

so

Pr(x = 0 ; lambda = 12) = e-12 = 6.1442 x 10-6

(b) Here the distribution of the time at which the first afternoon message arrived is exponential distribution with parameter = 1/3 hours-1

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