3. Four mutual friends are avid texters: at any time, each friend has a probability Xh+o(h)...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
3. Four mutual friends are avid texters: at any time, each friend has a probability Xh+o(h) of sending a text message in the next time interval of length h. Whenever any friend sends a message, it is addressed to one of the other three, with the recipient chosen at random with equal probability. Unknown to the four friends, their messaging platform is susceptible to a virus that spreads whenever an infected device sends a message to an uninfected device. Once infected, a device remains infected for an exponential time with mean 1/μ before security features remove the virus. Let X(t) be the number of infected devices at time t. The four friends do not have a group chat channel and only ever send single-recipient mes- sages. Messages sent to infected devices, or from one uninfected device to another, do not affect the virus. The friends have disabled app updates, so devices can be reinfected even after the virus has been removed. (a) Find the Q-matrix for the continuous time Markov chain (X(t): t ≥ 0). [5] the joint (b) Let J = inf {t > 0: X(t) ‡ X(0)} be the time of the first change in the number of infected devices. Suppose that initially 2 devices are infected. Calculat distribution of J and X(J). Give the average of time J, and the average number of devices infected at time J. [4] 3. Four mutual friends are avid texters: at any time, each friend has a probability Xh+o(h) of sending a text message in the next time interval of length h. Whenever any friend sends a message, it is addressed to one of the other three, with the recipient chosen at random with equal probability. Unknown to the four friends, their messaging platform is susceptible to a virus that spreads whenever an infected device sends a message to an uninfected device. Once infected, a device remains infected for an exponential time with mean 1/μ before security features remove the virus. Let X(t) be the number of infected devices at time t. The four friends do not have a group chat channel and only ever send single-recipient mes- sages. Messages sent to infected devices, or from one uninfected device to another, do not affect the virus. The friends have disabled app updates, so devices can be reinfected even after the virus has been removed. (a) Find the Q-matrix for the continuous time Markov chain (X(t): t ≥ 0). [5] the joint (b) Let J = inf {t > 0: X(t) ‡ X(0)} be the time of the first change in the number of infected devices. Suppose that initially 2 devices are infected. Calculat distribution of J and X(J). Give the average of time J, and the average number of devices infected at time J. [4]
Expert Answer:
Answer rating: 100% (QA)
a To find the Qmatrix for the continuoustime Markov chain Xt t 0 we need to determine the transition rates between different states of the system Lets ... View the full answer
Related Book For
Posted Date:
Students also viewed these accounting questions
-
Let X be a continuous random variable with values in [0, 2] and density fX. Find the moment generating function g(t) for X if (a) fX(x) = 1/2. (b) fX(x) = (1/2)x. (c) fX(x) = 1 (1/2)x. (d) fX(x) = |1...
-
Let X be a continuous random variable with values in [0,) and density fX. Find the moment generating functions for X if (a) fX(x) = 2e2x. (b) fX(x) = e2x + (1/2)e-x. (c) fX(x) = 4xe2x. (d) fX(x) = (...
-
Let X be a continuous random variable with mean (X) and variance 2(X), and let X* = (X )/ be its standardized version. Verify directly that (X*) = 0 and 2(X*) = 1.
-
TCP: the client sends only 1 message to the server hello from TCP Client and the server responds with the uppercase message. Update the program / make a simple chat program so that The client can...
-
Identify some of the instructions that investors can give brokers when trading securities. Under what circumstances would a limit order be appropriate? Why would an investor ever use a good til...
-
A home microwave oven uses electromagnetic waves with a wavelength of about 12.2 cm. Some 2.4-GHz cordless telephones suffer noisy interference when a microwave oven is sed nearby. Locate the waves...
-
Harold Fail owned a plot of land in Georgia known as Ebenezer Landing, where he operated a public boat ramp and parking lot. In 1999, Fail and Steve Bodiford entered into an oral agreement...
-
Installment-Sales Method Calculations, Entries Coffin Corporation appropriately uses the installment-sales method of accounting to recognize income in its financial statements. The following...
-
If a proton gains 6 x 10-12 J of electrical potential energy as it moves from point A to point B, what is the voltage difference between points A and B, and which point is at the higher potential?
-
On September 1, 201X, Dan Potter opened an auto repair shop. Here is his chart of accounts: Assets Liabilities Equity 101 Cash 201 Accounts Payable 301 Dan Potter, Capital 102 Accounts Receivable 302...
-
Use the figure below to answer the following questions. Price (dollars per jacket) 180 160 140 120 100 80 60 40 20 0 Figure 4 80 160 240 MC D MR 320 400 Quantity (jackets per day! a) Refer to Figure...
-
LIST THE WAYS for improving THE WEAKNESS OF Adjusting Depreciation Procedure?
-
7. Provide a suggestion of two goals: one long-term and one short-term goal for the future direction of Walmart. Include a justified rationale of the suggestions.
-
7. A uniform meter stick (100 cm) is loaded with the following masses: 110 g at 15.0 cm, 140 g at 60.0 cm, and 180 g at 90.0 cm. It was found that the center of gravity (balance point) of the system...
-
Lubbock National Bank processes loan applications through two clerks set up in series. The first clerk checks that the applicant has a proven track record of paying their loans which includes loan...
-
Light crude oil is imported and stored on site in a 10m high bunded tank with a floating roof. The crude oil pump is located in the bunded area. The crude oil is pumped via a pipe at the continuous...
-
If the f has at most one fixed point. Let f,g: [a,b] be continuous and differentlable for all x (a, b) Prove for all x (a, b),
-
A 6-lb shell moving with a velocity ?? v0k explodes at point D into three fragments which hit the vertical wall at the points indicated. Fragments A, B, and C hit the wall 0.010 s, 0.018 s, and 0.012...
-
If a disk has double interleaving, does it also need cylinder skew in order to avoid missing data when making a track-to-track seek? Discuss your answer.
-
Explain how time quantum value and context switching time affect each other, in a round-robin scheduling algorithm.
-
Write a shell script that produces a file of sequential numbers by reading the last number in the file, adding 1 to it, and then appending it to the file. Run one instance of the script in the...
-
One difference between accounting for a governmental (not-for-profit) unit and a commercial (for-profit) enterprise is that a governmental unit should a. Not record depreciation expense in any of its...
-
Carson Citys general fund issued purchase orders of $630,000 to vendors for supplies. Which of the following entries should the city make to record this transaction? Debit Credit Q. ENCUMBRANCES...
-
Belle Valley incurred $100,000 of salaries and wages for the month ended March 31, 20X2. How should this be recorded on that date? c. Expenditures Salaries and Wages Debit Vouchers Payable Salaries...
Study smarter with the SolutionInn App