Question 6:After research and observation the number of government system hackers active each day is arandom variable with Bin(3, 0.5) distrobution. If no hackers are active the probabilty of a systemfailure is 0.15. If one hacker is active the probability of a system failure is 0.3. If two or more hackersare active the probabilty of a system failure is 0.5(i)Conclude the total probability of a system failure on a given day. (Answer to 2 decimalplaces)Assuming there is a failure, what is the probabilty that no hackers are active.. (Answerto 2 decimal places)(ii)

Introduction: Denote Denote X as the number of government system hackers active on a randomly…

Answered: Question 6: After research and…

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...

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From a large consignment of clementine fruit destined for a UK supermarket the cus- toms office is making a check at the boarder. According to the sender the weight of the fruit belongs to an unknown distribution of mean 50 g and variance 16 g. If the cus- toms officer takes 100 fruits at random what is the probability that their total weight will be more than 5040 g. Justify any assumptions you make in your calculations.
A box contains 5 green and 3 orange balls. If three balls are taken at random with replacements, what is the variance number of orange balls? A. 45/8 B. 15/8 C. 1/8 D. 9/8
Give 7 other examples of random variables.
please send correct answer for Q4
Choose the correct definition of a random variable from the list below. A random variable is one whose values correspond to a scale with a countable number of values. one that occurs in one of two possible states, labeled success and failure. one that is measured to explain changes in the response variable. one whose values describe the outcome of some chance process. O one whose effect in an experiment cannot be distinguished from the effects of other variables.
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…

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