The most likely number of white corpuscles om a slide is 4 ,the probability of obtaining this number 4 is 0.190 , probability of obtaining at least two white corpuscles in total on the two slides is 0.999.
Attending to the first question
<h3>What is Poison Distribution ?</h3>Poisson Distribution is used for an independent event to find its probability in a fixed interval of time .
Let X be the number of white corpuscles on a slide, then X~Pois(4.5)
a) We have to find the most likely number of white corpuscles on a slide , which means expected value of Poise(4.5)
The expected value of Poisson distribution with mean λ is equal to λ.
Therefore the expected value is 4.5.
the number of corpuscles cannot be non-integer,
To find the most likely number in one experiment,
determine it between 4 and 5.
In the common case P(X=k) when X~Poise(λ) is equal to
, is a constant in terms of k
so the point is to find out what is greater : or
So, is greater
So, the most likely number of white corpuscles om a slide is 4.
b) the probability of obtaining this number 4 is
P(X = 4)
=
c) Let Y be the total number of corpuscles on two screens.
,
where - number of corpuscles on the first and second slide respectively.
Then Y = Poise(4.5 + 4.5) = Poise(9)
the probability, correct to three decimals places of obtaining at least two white corpuscles in total on the two slides
The goal is to find P(Y ≥ 2)
Therefore the probability less than 2 will be subtracted from the total probability i.e. 1
P(Y ≥ 2 ) = 1 - P (Y=0) - P(Y=1)
=
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