explain each briefly the THREE (3) Properties of the
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Enumerate and explain each briefly the THREE (3) Properties of the Poisson Process.
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- 5A time-series is a vector used to describe a process evolving as a function of time. Suppose c₁ € R³65 and C₂ € R³65 contains the number of cases of a virus over 365 consecutive days. Provide interpretations of the following mathematical statements (1 sentence per response). Interpretations should be in terms of virus cases, and not a re-statement of the mathematical expression. (a) (C₁)k+1 > (C₁)k for k = 1, 2, ..., 364. (b) c ₂ = 0 (c) ||c₁||1 > ||C₂||1, where || ||1 denotes the 1-norm.Q2 Cars arrive at a parking lot at a rate of 20 per hour. Assume that a Poisson process model is appropriate. Answer the following questions. No derivations are needed but a justification of your answers is necessary. Q2 (iv.) Assume that the lot opens at 8 a.m. what is the expected time at which the tenth car arrives at the parking lot. Q2(v.) What is the expected waiting time between the arrival of the 10th and 11th car? Q2(vi.) How is the waiting time between the arrival times of 10th and 12th car distributed? Write the density function of the waiting time.
- During registration at Tech every quarter, students in theDepartment of Management must have their coursesapproved by the departmental advisor. It takes the advisoran average of five minutes (exponentially distributed) toapprove each schedule, and students arrive at the adviser’s office at the rate of 10 per hour (Poisson distributed). Com-pute L, Lq, W, Wq, and . What do you think about this system? How would you change it?Probability and Stochastic Process Identify for the following 13.3 13.4 13.5 13.6 whether the process is discrete time or continuous time, discrete or continuous valuethe following calculations arise in certain highly simplified models of learning processes. Let X₁(t) and X₂(t) be independent Poisson processes having parameters 1 and 1 2, respectively (a) What is the probability that X₁(t) = 1 before X₂(t) = 1? (b) What is the probability that X₁(t) = 2 before X₂(t) = 2?
- A Poisson process {N(t);t≥0} has a rate of λ=6 per hour. The events that occur are classified as type 1 and type 2. When an event occurs, there is a 0.3 probability that it is a type 1 event. Assuming the event types are independent of each other; find the probability that (i) not more than two events of type 1 and not fewer than four events of type 2 occur in any given three hour period.(round off answer to one decimal point)On each trial of an experiment, a subject is presented with a constant soft noise, which is interrupted at some unpredictable time by a noticeably louder sound. The time it takes for the subject to react to this louder sound is recorded. The following list contains the reaction times (in milliseconds) for the 19 trials of this experiment: 171, 212, 285, 175, 202, 269, 193, 217, 164, 231, 261, 236, 186, 257, 271, 229, 250, 296, 226 Send data to calculator Find 20th and 75th percentiles for these reaction times. (If necessary, consult a list of formulas.) (a) The 20th percentile: milliseconds (b) The 75th percentile: millisecondsOn each trial of an experiment, a subject is presented with a constant soft noise, which is interrupted at some unpredictable time by a noticeably louder sound. The time it takes for the subject to react to this louder sound is recorded. The fallowing list contains the reaction times (in milliseconds) for the 16 trials of this experiment: 241, 271. 261, 164, 257, 193. 186, 222, 226, 212, 152, 273, 217, 171, 175, 202 Send date to caleulator Find 40 and 75" percentiles for these reaction times. (a) The 40 percentile: Imilliseconds (b) The 75t percentile: miliseconds
- On each trial of an experiment, a subject is presented with a constant soft noise, which is interrupted at some unpredictable time by a noticeably louder sound. The time it takes for the subject to react to this louder sound is recorded. The following list contains the reaction times (in milliseconds) for the 15 trials of this experiment: 212, 236, 217, 235, 164, 257, 175, 285, 202, 193, 231,152, 269, 296, 186 Send data to calculator Find 30th and 75th percentiles for these reaction times.Comparing the mea Español On each trial of an experiment, a participant is presented with a constant soft noise that is interrupted by a slightly louder sound. The time it takes for the participant to react to the louder sound is recorded. The following list contains the reaction times (in milliseconds) for 25 trials of this experiment. 190, 202, 212, 221, 243, 250, 257, 271, 288, 288, 288, 309, 311, 315, 323, 335, 359, 364, 388, 418, 440, 476, 526, 603, 756 Send data to calculator Frequency ↑ 124 10- 8+ 64 4- 24 04 150 11 Send data to Excel Answer the questions below. 10 2 300 450 600 Reaction time (in milliseconds) (a) Which measures of central tendency do not exist for this data set? Choose all that apply. Check (b) Suppose that the measurement 190 (the smallest measurement in the data set) were replaced by 72. Which measures of central tendency would be affected by the change? Choose all that apply. (c) Suppose that, starting with the original data set, the largest measurement were…A sleep researcher is interested in learning about how to help people fall asleep faster at night without taking medicine. She asks n = 13 individuals to wear a device to bed for two weeks straight. Half of the participants were asked to spray their pillows with a lavender mist for the first week then sleep with a regular "unscented" pillow for the second week. The other half of the participants were asked to do the same thing, but in the opposite order: unscented pillow then lavender misted pillow. Testing at an alpha level of a = .01, she expects the lavender scented pillow to decrease the amount of time it takes people to fall asleep. State the Hypotheses 2 3 4 5 Ho: Subject 6 7 H₁: 8 9 10 11 12 13 MD= = Determine the critical region and draw it on the distribution above: Calculate the test statistic using the following sample data below: 360 sec 420 sec 480 sec tcritical = Regular Lavender Pillow Pillow 420 sec 420 sec 480 sec 480 sec 360 sec 360 sec 420 sec 420 sec 420 sec 420 sec…
