Scientists are using a device to count neutrinos. Every time a neutrino is detected, the sensor...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Scientists are using a device to count neutrinos. Every time a neutrino is detected, the sensor will record the time. Neutrinos are assumed to arrive independently with a constant likelihood of arrival over the course of the experiment. The experiment lasts for one year. (a) What would be a good model for the number of neutrinos counted in this one experiment? What do the parameter (s) mean? (b) Now the scientists want to be able to say how long they are expected to wait before the next neutrino is detected. What distribution would you recommend to be used and why? Interpret the parameter(s). (c) After some puzzling results, a scientist realizes that the tool for counting neutrinos does not always get triggered. It turns out that the transistor in the equipment requires a high voltage to trigger the count, but sometimes the trigger will happen also at lower voltages. Below 5 micro volts the transistor never triggers, then the probability of triggering increases monotonically until 5.5 micro volts, at which point the transistor always triggers. The scientist wants to use a probabilistic model for the level of voltage when there is uncer- tainty about whether the transistor triggers the count or not. What is a good distribution and what range would its parameter(s) take to match the described behaviour of the transistor? Hints: • It is possible to change the support of a random variable (i.e. the set of values that can be taken on by the random variable) by a suitable transformation of that random variable. • It may be helpful in answering this question to explore the shape of the densities for distributions we studied in class, for example, using the applets provided under the following link: http://homepage.stat.uiowa.edu/~mbognar/. Scientists are using a device to count neutrinos. Every time a neutrino is detected, the sensor will record the time. Neutrinos are assumed to arrive independently with a constant likelihood of arrival over the course of the experiment. The experiment lasts for one year. (a) What would be a good model for the number of neutrinos counted in this one experiment? What do the parameter (s) mean? (b) Now the scientists want to be able to say how long they are expected to wait before the next neutrino is detected. What distribution would you recommend to be used and why? Interpret the parameter(s). (c) After some puzzling results, a scientist realizes that the tool for counting neutrinos does not always get triggered. It turns out that the transistor in the equipment requires a high voltage to trigger the count, but sometimes the trigger will happen also at lower voltages. Below 5 micro volts the transistor never triggers, then the probability of triggering increases monotonically until 5.5 micro volts, at which point the transistor always triggers. The scientist wants to use a probabilistic model for the level of voltage when there is uncer- tainty about whether the transistor triggers the count or not. What is a good distribution and what range would its parameter(s) take to match the described behaviour of the transistor? Hints: • It is possible to change the support of a random variable (i.e. the set of values that can be taken on by the random variable) by a suitable transformation of that random variable. • It may be helpful in answering this question to explore the shape of the densities for distributions we studied in class, for example, using the applets provided under the following link: http://homepage.stat.uiowa.edu/~mbognar/.
Expert Answer:
Answer rating: 100% (QA)
Answer Solution a This model is detected or arrived for Nautrinos reco... View the full answer
Related Book For
Posted Date:
Students also viewed these accounting questions
-
A useful unidirectional sensing device is the photo emitter sensor [15]. A light source is sensitive to the emitter current flowing and alters the resistance of the photo sensor. Both the light...
-
Scientists at a major pharmaceutical firm conducted an experiment to study the effectiveness of an herbal compound to treat the common cold. They exposed each patient to a cold virus, then gave them...
-
One measure of airline performance is on-time arrival rates. For May 2009 the on-time arrival rates of domestic flights for the 19 largest U.S. airlines were as follows: a. Find the range and the...
-
Suppose Nordic Boots was making production decisions for the following six boots: ot Price E(Demand) Std. Dev (Demand) Co Cu Exp. Profit Max. Profit A 220 1000 400 35.2 52.8 1101 39201 52800 230 2000...
-
In a certain communication system, bits are encoded into blocks of length 128 bits. Error correction techniques are used such that the block will be decoded correctly as long as no more than 7 of the...
-
The presence of carbon monoxide (CO) in flue gases means: (a) High excess air (b) Poor combustion (c) High thermal efficiency (d) All of the above
-
What ethical standards paralegals must follow?
-
At August 31, Oscar Company has a cash balance per books of $8,500 and the following additional data from the bank statement: charge for printing Oscar Company checks $35, interest earned on checking...
-
Find the quotient Z1 - of the complex numbers. Leave your answer in polar form. Express the argument as an angle Z2 between 0 and 360. Z1 = cos 90 + i sin 90 Z = cos 230 + i sin 230 Z1 = COS Z2 O + i...
-
The following table summarizes the operating results for Bene Petits first year of operations: Bene Petit First year operating data: Single (1 serving) Dual (2 servings) Family (4 servings) Total...
-
Hacienda Farms, Ltd., was organized as a limited partnership with Ricardo de Escantilla as the general partner and James L. Russell and H.W. Andrews as limited partners. The partnership raised...
-
What is the New York Stock Exchange (NYSE)?
-
What is a firms enterprise value, and what does it measure?
-
What is the diluted earnings per share?
-
What is the balance sheet identity?
-
In what two cases is the internal rate of return easy to calculate?
-
The Cutting Department of Karachi Carpet Company provides the following data for January. Assume that all materials are added at the beginning of the process. Work in process, January 1, 14,800...
-
What are the before image (BFIM) and after image (AFIM) of a data item? What is the difference between in-place updating and shadowing, with respect to their handling of BFIM and AFIM?
-
A simple closed-loop control system has been proposed to demonstrate proportional-integral (PI) control of a windmill radiometer [27]. The windmill radiometer is shown in Figure DP10.8(a) and the...
-
A position control system for a DC motor is shown in Figure AP7.8. Obtain the root locus for the velocity feedback constant K, and select K so that all the roots of the characteristic equation are...
-
A temperature system has a process transfer function and a sampling period T of 0.5 second. (a) Using D(z) = K, select a gain K so that the system is stable, (b) The system may be slow and over...
-
What is reaction coordinate? What is its significance in chemical reaction?
-
Show that for steady state flow process, \(\Delta H=Q-W_{S}\).
-
An ideal gas \(\left(C_{P}=5, C_{V}=3 ight)\) is changed from \(1 \mathrm{~atm}\) and \(22.4 \mathrm{~m}^{3}\) to \(10 \mathrm{~atm}\) and 2.24 \(\mathrm{m}^{3}\) by the reversible process of heating...
Study smarter with the SolutionInn App