Viktoria's Shower & Plumbing receives customer inquiries via SMS or email. Inquiry is made every working day Monday to F

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Viktoria S Shower Plumbing Receives Customer Inquiries Via Sms Or Email Inquiry Is Made Every Working Day Monday To F 1 (73.36 KiB) Viewed 94 times

Viktoria's Shower & Plumbing receives customer inquiries via SMS or email. Inquiry is made every working day Monday to Friday in the period from 8.00 - 14.00. Times for customer inquiries can be modelled with a Poisson process in time, and inquiries arrive in average at 20-minute intervals. Time unit for the process: 1 minute. The continuous stochastic variable T describes the length of the time interval between 2 on each other the following inquiries. a) State the distribution of T as well as f (t), F (t), E (T) and Var (T). Calculate the median of T. b) Find the probability that no customer inquiries will arrive within one time interval of 30 minutes. c) Find the probability that 2 customer inquiries will arrive within a time interval of 10 minutes. d) Find the probability that the first customer inquiry of the day will arrive in the period between at 8.05 and at 8.10. The daily 6-hour opening time at 8.00am to 14.00pm for customer inquiries corresponds to 12 time intervals of 30 minutes length. The stochastic variable X describes the number of 30 minute intervals without customer inquiries in during a working week. e) State the distribution of X and calculate P ( X2).