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How can the Poisson distribution be applied to a continuous frequency distribution?
Let L(t) be the instantaneous average rate of occurrences per unit time, at time t. So, for the ordinary Poisson distribution with parameter L, we just have L(t)=L for all t.
Let I be the integral of L(t) dt over a certain time interval [0,T], say.
Then, assuming that L(t) is continuous, or maybe just Riemann integrable, the total number of occurrences during [0,T] simply follows a Poisson distribution with parameter I. This is the simple answer one might expect.
To prove this (SKETCH: further estimates are needed to make this really rigorous): divide [0,T] into many small intervals [tj, tj+1). In each interval, the number of occurrences is approximately Poisson with parameter L(tj)(tj+1-tj).
The occurrences in each small interval are all independent of each other; hence the total number in [0,T], which is the sum of all these, follows a Poisson distribution with parameter the sum of L(tj)(tj+1-tj).
As you make the maximum size of the intervals shrink to zero, this sum tends towards I, the Riemann integral of L(t)dt over [0,T], as required.
What else can I help you with?
What is the definition line?
A thin continuous mark, as that made by a pen, pencil, or brush applied to a surface.
What is difference bw integral and summetion?
Usually an integral is applied to a continuous function (eg temperature) while summations are applied to discrete functions (eg. car manufacture or crowd capacity?) They both represent 'the area under the curve' in some sense.
What is the value of Poisson's ratio of plywood?
The value of Poisson's ratio for plywood typically ranges from 0.2 to 0.4, depending on the specific type and orientation of the wood fibers. Plywood is an engineered wood product made by gluing together layers of veneer, which can influence its mechanical properties. The ratio reflects the material's tendency to expand or contract in directions perpendicular to the applied stress. For precise applications, it's best to consult specific material data sheets or conduct tests on the particular plywood in question.
How is frequency expressed?
Frequency can be applied to any kind of motion that is repetitive. It answers the question; "how frequent does the cycle repeat itself?" Then it is expressed by counting how often the motion repeats in a certain amount of time and dividing that count by the time. For example if 12 complete waves (or cycles) pass a point in 6 seconds then the frequency is 12/6 = 2 cycles/sec. The unit of 1 cycle/sec is called a Hertz so the frequency would also be expressed as 2 Hertz or 2 Hz.
When studying the simultaneous responses to two categorical questions you should set up?
When studying the simultaneous responses to two categorical questions, you should set up a contingency table. This table allows you to display the frequency distribution of the responses for each combination of the categories from the two questions. By analyzing this table, you can identify any potential associations or patterns between the two categorical variables. Additionally, statistical tests such as the Chi-square test can be applied to assess the significance of these associations.
What are the Situations wherein poisson distribution is applied?
The Poisson distribution may be used when studying the number of events that occur in a given interval of time (or space). These events must occur at a constant rate, be independent of the time since the previous occurrence.
Is the normal probability distribution applied to a continuous random variable?
Yes.
Why AM is high frequency in communication why not low frequency?
A.m. can be applied to a carrier of any frequency.
What is meant by free running frequency in phase locked loop?
The VCO is a special type of oscillator that has a frequency controlled by an applied voltage.The frequency of the VCO without any control signal applied is called the free running frequency.
What occurs if the frequency of a force applied to system matches the natural frequency ofvibration of the system?
Resonant
How are FM signal generated?
There are several methods for generating FM signals but they all basically involve an oscillator with an electrically adjustable frequency. This type of oscillator uses an input voltage to affect the frequency of its output. For example, when the applied voltage increases, the oscillator output frequency increases and when the applied voltage decreases, the oscillator output frequency decreases as well. If no voltage is applied to the oscillator its output will be a signal at its centre frequency. The amount of frequency variations is deviated around the oscillators' centre frequency.
What is the difference between resonant frequency and natural frequency?
Resonant frequency is the frequency at which an object naturally vibrates when energy is applied, while natural frequency is the frequency at which an object vibrates without any external force.
Is a wave's frequency is indirectly proportional to the energy applied?
No. Energy content of wave packet is directly proportional to the frequency.
What is a discrete and continuous series?
how is time series applied in the business world today
When the frequency of an applied voltage is increased the capacitive reactance of a circuit will?
Since capacitive reactance is inversely-proportional to the supply frequency, as the frequency is increased, the reactance will decrease.
Distribution of Logic?
Yes, it has clearly not been applied to the phrasing of this question.
Why is a correction factor of x or - 0.5 needed?
The answer depends on the context. In probability or statistics, when using a continuous distribution as an approximation for a discrete distribution it is advisable to use 0.5 as a "continuity correction". This is to allow for the fact that the discrete variable usually cannot take values between integers. In other situations a correction may be applied to allow for measurement error.
