The Poisson distribution can be written as P(k,p)=/k! (see e.g. Melissinos & Napolitano Pg. 438). This...
The Poisson distribution can be written as P(k,p)=
/k!
(see e.g. Melissinos & Napolitano Pg. 438). This distribution
gives the probability that an event happens exactly k times during
an experiment, with p the average probability that this event would
happen if the experiment was repeated many times. Thus, if R is the
average rate that photons enter a double-slit experiment, the
average probability of finding a photon in the experiment can be
written as p = LR/c. Here c is the speed of light and L=0.50 m is
the distance from the double-slit to the detector.
Question 1. Suppose that the rate of photons entering the double-slit experiment is R = 4261913 photons/s. The percentage of time that there is only a single photon (k=1) in the experiment is ____ %.
Question 2. Suppose that the rate of photons entering the double-slit experiment is R = 3834109 photons/s. The percentage of time that there is more than one photon (k>1) in the experiment is ____ %.
Homework Answers
Request Answer!
We need at least 10 more requests to produce the answer.
0 / 10 have requested this problem solution
The more requests, the faster the answer.
Add Answer to:
The Poisson distribution can be written as P(k,p)=/k!
(see e.g. Melissinos & Napolitano Pg. 438). This...
Homogeneous Poisson process N(t) counts events occurring in a time interval and is characterized by Ņ(0)-0...
Homogeneous Poisson process N(t) counts events occurring in a time interval and is characterized by Ņ(0)-0 and (t + τ)-N(k) ~ Poisson(λτ), where τ is the length of the interval (a) Show that the interarrival times to next event are independent and exponentially distributed random variables (b) A random variable X is said to be memoryless if P(X 〉 s+ t | X 〉 t) = P(X 〉 s) y s,t〉0. that this property applies for the interarrival times if...
Recall that a discrete random variable X has Poisson distribution with parameter λ if the probability...
Recall that a discrete random variable X has Poisson
distribution with parameter λ if the probability mass function of
X
Recall that a discrete random variable X has Poisson distribution with parameter λ if the probability mass function of X is r E 0,1,2,...) This distribution is often used to model the number of events which will occur in a given time span, given that λ such events occur on average a) Prove by direct computation that the mean of...
This question is about a discrete probability distri Poisson distribution, the one which in fact mo-...
This question is about a discrete probability distri Poisson distribution, the one which in fact mo- bution known as the Poisson distribution. Let r be a discrete random variable that can take the values 0, 1,2,... A quantity r is said to be Poisson distributed if the probability P(x) of obtaining z is tivated Poisson, was connected with the rare event of someone being kicked to death by a horse in the Prussian army. The number of horse-kick deaths of...
The Binomial and Poisson Distributions Both the Binomial and Poisson Distributions deal with discrete data where...
The Binomial and Poisson Distributions Both the Binomial and Poisson Distributions deal with discrete data where we are counting the number of occurrences of an event. However, they are very different distributions. This problem will help you be able to recognize a random variable that belongs to the Binomial Distribution, the Poisson Distribution or neither. Characteristics of a Binomial Distribution Characteristics of a Poisson Distribution The Binomial random variable is the count of the number of success in n trials: number of...
Any help? 2. The Prussian horse-kick data: The derivation of the Poisson distribution that we did...
Any help?
2. The Prussian horse-kick data: The derivation of the Poisson distribution that we did in class is due to Poisson. However, this distribution did not see much application until a text by Bortkiewicz in 1898. One famous example from that text is the use of the “Prussian horse-kick data" to illustrate how the Poisson distribution may help evaluate whether rare events are really occurring independently or randomly. Bortkiewicz studied the distribution of 122 men kicked to death by...
During tax season the IRS hires seasonal workers to help answer the questions of taxpayers who...
During tax season the IRS hires seasonal workers to help answer the questions of taxpayers who call a special toll-free number for information. Suppose that calls to this line occur at an average rate of 60 calls per hour and follow a Poisson distribution. An IRS worker can handle an average of 5 calls per hour with service times, exponentially distributes. Assume that there are 10 IRS workers and when they are all busy, the phone system can keep 5...
Ch 04: Mastery Assignment - Introduction to Probability 4. Scrabble SCRABBLE is a word game in...
Ch 04: Mastery Assignment - Introduction to Probability 4. Scrabble SCRABBLE is a word game in which two to four players score points by forming words from individual lettered tiles on a game board marked with a 15 by 15 grd. The words are formed across and down in crossword puzzle fashion and must appear in a standard dictionary. There are 100 tiles in all, including 2 blank tiles that serve as wild cards and can take on the value...
Homogeneous Poisson process N(t) counts events occurring in a time interval and is characterized by Ņ(0)-0 and (t + τ)-N(k) ~ Poisson(λτ), where τ is the length of the interval (a) Show that the interarrival times to next event are independent and exponentially distributed random variables (b) A random variable X is said to be memoryless if P(X 〉 s+ t | X 〉 t) = P(X 〉 s) y s,t〉0. that this property applies for the interarrival times if...
Recall that a discrete random variable X has Poisson
distribution with parameter λ if the probability mass function of
X
Recall that a discrete random variable X has Poisson distribution with parameter λ if the probability mass function of X is r E 0,1,2,...) This distribution is often used to model the number of events which will occur in a given time span, given that λ such events occur on average a) Prove by direct computation that the mean of...
This question is about a discrete probability distri Poisson distribution, the one which in fact mo- bution known as the Poisson distribution. Let r be a discrete random variable that can take the values 0, 1,2,... A quantity r is said to be Poisson distributed if the probability P(x) of obtaining z is tivated Poisson, was connected with the rare event of someone being kicked to death by a horse in the Prussian army. The number of horse-kick deaths of...
Any help?
2. The Prussian horse-kick data: The derivation of the Poisson distribution that we did in class is due to Poisson. However, this distribution did not see much application until a text by Bortkiewicz in 1898. One famous example from that text is the use of the “Prussian horse-kick data" to illustrate how the Poisson distribution may help evaluate whether rare events are really occurring independently or randomly. Bortkiewicz studied the distribution of 122 men kicked to death by...
Ch 04: Mastery Assignment - Introduction to Probability 4. Scrabble SCRABBLE is a word game in which two to four players score points by forming words from individual lettered tiles on a game board marked with a 15 by 15 grd. The words are formed across and down in crossword puzzle fashion and must appear in a standard dictionary. There are 100 tiles in all, including 2 blank tiles that serve as wild cards and can take on the value...
Most questions answered within 3 hours.
-
A dragon biologist is setting up an experimental population of
1000 individuals. In dragons, pointy crests...
asked 44 seconds ago -
A uniform thin rod of length 0.851 m is hung from a horizontal
nail passing through...
asked 10 minutes ago -
A 747 has a cruising speed of 235 m/s at a height of 10,700
meters. The...
asked 19 minutes ago -
Part 3: Arrows
Write a python program that prompts the user for a number of
columns,...
asked 26 minutes ago -
Need help answering these questions!!
1. What economic concept do you find most interesting in
Macroeconomics?...
asked 30 minutes ago -
1. Nimbus, Inc. produces and sells brooms. This table shows the
relationship between the number of...
asked 34 minutes ago -
A gas occupies 200. mL in a piston. If the pressure of the
piston were decreased...
asked 50 minutes ago -
A fossil is found to have a 14C level of 71.0% compared to
living organisms. How...
asked 54 minutes ago -
Many communist or socialist countries have a department that
addresses public health as well as the...
asked 56 minutes ago -
the following questions are either true or false answers
1. The Central Limit Theorem allows one...
asked 56 minutes ago -
The patient recovery time from a particular surgical procedure
is normally distributed with a mean of...
asked 1 hour ago -
Human relations refer to the way a company arranges people,
jobs, and communications so that work...
asked 1 hour ago