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...

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 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?