An information center provides services in bilingual languages; requests for service arrive by telephone. Major language service requests and minor language service requests arrive according to independent Poisson processes with respective rate λ1 and λ2 requests per hour.
The service time for each request is exponentially distributed with a mean of 1/μ1 minutes for major language request and a mean of 1/μ2 minutes for minor language request.
1. The probability that in the next hour a total of n service requests will arrive?
2. The probability density of service time of an arbitrarily chosen service request?