0
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.
Add your answer:
Earn +20 pts
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.
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.
How you can use negative binomial distribution in everyday life?
The negative binomial can be applied in any situation in which there is a series of independent trials, each of which can result in either of just two outcomes. The distribution applies to the number of trials that occur before the designated outcome occurs. For example, if you start flipping a fair coin repeatedly the negative binomial distribution gives the number of times you must flip the coin until you see 'heads'. There are also 'everyday' applications in inventory control and the insurance industry. Please see the link.
Does an accountant job fall under applied math or pure math?
It is applied math. Math is the purest form there is. psychology is applied biology, which is applied chemistry, which is applied physics, which is applied math, which is pure PURE
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.
Is having a tattoo continuous or discontinuous?
Having a tattoo is continuous because the design is applied to the skin in a continuous manner, creating a permanent mark. The ink flows smoothly without breaks or interruptions.
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.
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
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.
Distribution of Logic?
Yes, it has clearly not been applied to the phrasing of this question.
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.
