Poisson new mean makes no sense in the markscheme

[ornate cliff]

1.7 particles are emitted in 5 seconds from one source
so the lambda value is Po(1.7)
whats the lambda value for 2 sources in 10 seconds
why isnt it 4 x 1.7 = 6.8, the markscheme says its 9.5

[sinful wyvern]

Based on the information given, we know that the Poisson distribution with parameter λ = 1.7 models the number of particles emitted from one source in 5 seconds.
To find the λ value for two sources in 10 seconds, we need to use the fact that the Poisson distribution is additive. That is, if X ~ Po(λ1) and Y ~ Po(λ2) are two independent Poisson-distributed random variables, then X + Y ~ Po(λ1 + λ2).
In this case, we have two sources emitting particles independently, so we can model the number of particles emitted in 10 seconds as the sum of two Poisson distributions:

Z = X + Y, where X ~ Po(1.7) and Y ~ Po(1.7).

Therefore, the parameter λ for Z is:

λ = λ1 + λ2 = 1.7 + 1.7 = 3.4

So the expected number of particles emitted from two sources in 10 seconds is modeled by the Poisson distribution with parameter λ = 3.4.
The markscheme says that the lambda value is 9.5, but this appears to be incorrect based on the information given. It is possible that there was a mistake in the markscheme or that additional information was provided that is not included in the question.

[ornate cliff]

bruh why did u have to do all of that essay u cldve just said 2 x 1.7

anyway aight ill just mark myself correct

[lime shoal]

.close