Suppose the number of photons emitted by an atom during a one-minute time window can be modeled as a Poisson random variable with parameter λ = 2. Now, suppose you watch the atomfor two minutes, and the number of emitted photons in each minute is an independent Poisson process. Calculate the probability that you see exactly one photon during the two minutes. (Hint: this is the probability that you see no photons in the first minute and one photon in the second minute, plus the probability that you see one photon in the first minute and no photons in the second minute.) Similarly calculate the probability that you see exactly two photons during the two minutes.Compare these probabilities to the probabilities that a Poisson random variable with parameter λ= 4 takes the value one, or two. Are they the same?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Suppose the number of photons emitted by an atom during a one-minute time window can be modeled as a Poisson random variable with parameter λ = 2. Now, suppose you watch the atom
for two minutes, and the number of emitted photons in each minute is an independent Poisson process. Calculate the
Compare these probabilities to the probabilities that a Poisson random variable with parameter λ= 4 takes the value one, or two. Are they the same?
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