The number of emails a professor receives per day is observed to be a Poisson random variable with variance 81. The professor replies to each email with probability 2/3, independently of all other emails, and each reply takes five minutes to write. What is the expected length of time spent writing email replies per day (to the nearest minute)?

The number of emails a professor receives per day is observed to be a Poisson random variable with variance 81. The professor replies to each email with probability 2/3, independently of all other emails, and each reply takes five minutes to write. What is the expected length of time spent writing email replies per day (to the nearest minute)?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

Data from 14 cities were combined for a 20-year period, and the total 280 city-years included a total of 87 homicides. After finding the mean number of homicides per city-year, find the probability that a randomly selected city-year has the following numbers of homicides, then compare the actual results to those expected by using the Poisson probabilities: Homicides each city-year a. 0 b. 1 C. 2 d. 3 e. 4 Actual results 205 64 10 1 0 a. P(0) = (Round to four decimal places as needed.) b. P(1) = (Round to four decimal places as needed.) c. P(2) = (Round to four decimal places as needed.) d. P(3)= (Round to four decimal places as needed.) e. P(4)= (Round to four decimal places as needed.)
A farmer has six geese, each of which lays an egg with probability 2/3 (independently of all the other geese). Suppose that the farmer sells each egg for five gold coins. What is the variance of the number of coins received?
A large ski mountain has a fleet of 4 snowmobiles it uses during the winter season. It believes that the time between consecutive repair operations for a single snowmobile is an exponential random variable with a mean of .75 weeks. There are two dedicated technicians that are capable of repairing the snowmobiles. A broken down snowmobile will be repaired by one of these technicians (when one becomes available) and the repair time of a snowmobile can be modeled as an exponential random variable with a mean of .4 weeks. (a) Describe a queueing system model of the repair operations of the snowmobiles by answering the following questions: What are the customers in the queueing system? What are the servers and what service is being provided? b) Provide the rate transition diagram of the birth and death process that captures the queueing system. Be sure to provide λn and µn for each relevant value of n and your logic behind any calculations used to obtain them (c) Provide the…
The average amount of time until a car accident on a particular 60 mile stretch of road is 30 minutes. Assume(unreasonably) that car accidents are independent, the time to a car accident is exponentially distributed, and that two accidents cannot occur at the same time. a. What is the probability of a car accident occurring in the first hour?b. What is the probability of a car accident occurring between 15 and 45 minutes? c. What is the variance of the time until a car accident occurs? If a car accident has not happened in 2 hours, what is the probability it will happen in the next hour? DO NOT USE THE INTEGRATION METHOD PLEASE.
A survey of prison guards shows that their average starting hourly wage is $30 and the variance is 9. If prison guard is selected, what is the probability that his/her hourly wage will be greater than $27 but less than $35?